Help prove this basic trig identity please!If $sintheta + sinphi = a$ and $costheta + cosphi = b$, then...
I seem to dance, I am not a dancer. Who am I?
Should I be concerned about student access to a test bank?
Help prove this basic trig identity please!
Unfrosted light bulb
How does 取材で訪れた integrate into this sentence?
What does Deadpool mean by "left the house in that shirt"?
Maths symbols and unicode-math input inside siunitx commands
Do I need to consider instance restrictions when showing a language is in P?
How to define limit operations in general topological spaces? Are nets able to do this?
Can a wizard cast a spell during their first turn of combat if they initiated combat by releasing a readied spell?
Do US professors/group leaders only get a salary, but no group budget?
Describing a chess game in a novel
Is there a term for accumulated dirt on the outside of your hands and feet?
Using Past-Perfect interchangeably with the Past Continuous
Turning a hard to access nut?
Can other pieces capture a threatening piece and prevent a checkmate?
What favor did Moody owe Dumbledore?
World War I as a war of liberals against authoritarians?
What does "mu" mean as an interjection?
Bash - pair each line of file
How could an airship be repaired midflight?
Synchronized implementation of a bank account in Java
Why is there so much iron?
Should I use acronyms in dialogues before telling the readers what it stands for in fiction?
Help prove this basic trig identity please!
If $sintheta + sinphi = a$ and $costheta + cosphi = b$, then $sin(theta+phi) = ???$If $ sin alpha + sin beta = a $ and $ cos alpha + cos beta = b $ , then show that $sin(alpha + beta) = frac {2ab } { a^2 + b^2} $Trig equation help pleaseHelp With Double Angles And Trig Identity ProblemProve Trig IdentityHow to solve this trigonometric identity?Prove the following Trig Identity with reciprocalsHelp needed in verifying a trigonometric identityHow do I prove this seemingly simple trigonometric identityTrig Identity Proof $frac{1 + sintheta}{costheta} + frac{costheta}{1 - sintheta} = 2tanleft(frac{theta}{2} + frac{pi}{4}right)$If $x costheta+ysintheta=a$ and $xsintheta-ycostheta=b$, then $tantheta=frac{bx+ay}{ax-by}$. (Math Olympiad)Precalc Trig Identity, verify: $1 + cos(x) + cos(2x) = frac 12 + frac{sin(5x/2)}{2sin(x/2)}$
$begingroup$
I'm really stuck trying to answer this question and have spent endless hours doing so.
If $a=sin(theta)+cos(phi)$ and, $b=cos(theta)+sin(phi)$, prove that $cos(theta-phi)=frac{2ab}{a^2+b^2}$.
I've tried working LHS to RHS and couldn't get, I've also tried RHS to LHS and still couldn't get it, and advice or help would be much appreciated please.
I've also tried going $ab=...$ and then trying to get it from there, that didn't come to fruition either.
trigonometry
asked 4 hours ago
Avinash ShastriAvinash Shastri
184
New contributor
Avinash Shastri is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
add a comment |
$begingroup$
I'm really stuck trying to answer this question and have spent endless hours doing so.
If $a=sin(theta)+cos(phi)$ and, $b=cos(theta)+sin(phi)$, prove that $cos(theta-phi)=frac{2ab}{a^2+b^2}$.
I've tried working LHS to RHS and couldn't get, I've also tried RHS to LHS and still couldn't get it, and advice or help would be much appreciated please.
I've also tried going $ab=...$ and then trying to get it from there, that didn't come to fruition either.
trigonometry
asked 4 hours ago
Avinash ShastriAvinash Shastri
184
New contributor
Avinash Shastri is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
$begingroup$
Welcome to Math Stack Exchange. Do you know the formula for cosine of a difference?
$endgroup$
– J. W. Tanner
4 hours ago
$begingroup$
Yes, $cos(theta-phi)=cos(theta)cos(phi)+sin(theta)sin(phi)$, and I went much further but was not able to poduce anything useful in the sense of the proof.
$endgroup$
– Avinash Shastri
4 hours ago
$begingroup$
Set $theta=dfracpi2-psi$ and use math.stackexchange.com/questions/1833153/… or math.stackexchange.com/questions/2021356/…
$endgroup$
– lab bhattacharjee
2 hours ago
add a comment |
$begingroup$
I'm really stuck trying to answer this question and have spent endless hours doing so.
If $a=sin(theta)+cos(phi)$ and, $b=cos(theta)+sin(phi)$, prove that $cos(theta-phi)=frac{2ab}{a^2+b^2}$.
I've tried working LHS to RHS and couldn't get, I've also tried RHS to LHS and still couldn't get it, and advice or help would be much appreciated please.
I've also tried going $ab=...$ and then trying to get it from there, that didn't come to fruition either.
trigonometry
asked 4 hours ago
Avinash ShastriAvinash Shastri
184
New contributor
Avinash Shastri is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I'm really stuck trying to answer this question and have spent endless hours doing so.
If $a=sin(theta)+cos(phi)$ and, $b=cos(theta)+sin(phi)$, prove that $cos(theta-phi)=frac{2ab}{a^2+b^2}$.
I've tried working LHS to RHS and couldn't get, I've also tried RHS to LHS and still couldn't get it, and advice or help would be much appreciated please.
I've also tried going $ab=...$ and then trying to get it from there, that didn't come to fruition either.
trigonometry
trigonometry
asked 4 hours ago
Avinash ShastriAvinash Shastri
184
New contributor
Avinash Shastri is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
Avinash ShastriAvinash Shastri
184
New contributor
Avinash Shastri is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
Avinash ShastriAvinash Shastri
184
New contributor
Avinash Shastri is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 4 hours ago
Avinash ShastriAvinash Shastri
184
asked 4 hours ago
Avinash ShastriAvinash Shastri
184
184
New contributor
Avinash Shastri is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Avinash Shastri is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Avinash Shastri is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$begingroup$
Welcome to Math Stack Exchange. Do you know the formula for cosine of a difference?
$endgroup$
– J. W. Tanner
4 hours ago
$begingroup$
Yes, $cos(theta-phi)=cos(theta)cos(phi)+sin(theta)sin(phi)$, and I went much further but was not able to poduce anything useful in the sense of the proof.
$endgroup$
– Avinash Shastri
4 hours ago
$begingroup$
Set $theta=dfracpi2-psi$ and use math.stackexchange.com/questions/1833153/… or math.stackexchange.com/questions/2021356/…
$endgroup$
– lab bhattacharjee
2 hours ago
add a comment |
$begingroup$
Welcome to Math Stack Exchange. Do you know the formula for cosine of a difference?
$endgroup$
– J. W. Tanner
4 hours ago
$begingroup$
Yes, $cos(theta-phi)=cos(theta)cos(phi)+sin(theta)sin(phi)$, and I went much further but was not able to poduce anything useful in the sense of the proof.
$endgroup$
– Avinash Shastri
4 hours ago
$begingroup$
Set $theta=dfracpi2-psi$ and use math.stackexchange.com/questions/1833153/… or math.stackexchange.com/questions/2021356/…
$endgroup$
– lab bhattacharjee
2 hours ago
$begingroup$
Welcome to Math Stack Exchange. Do you know the formula for cosine of a difference?
$endgroup$
– J. W. Tanner
4 hours ago
$begingroup$
Welcome to Math Stack Exchange. Do you know the formula for cosine of a difference?
$endgroup$
– J. W. Tanner
4 hours ago
$begingroup$
Yes, $cos(theta-phi)=cos(theta)cos(phi)+sin(theta)sin(phi)$, and I went much further but was not able to poduce anything useful in the sense of the proof.
$endgroup$
– Avinash Shastri
4 hours ago
$begingroup$
Yes, $cos(theta-phi)=cos(theta)cos(phi)+sin(theta)sin(phi)$, and I went much further but was not able to poduce anything useful in the sense of the proof.
$endgroup$
– Avinash Shastri
4 hours ago
$begingroup$
Set $theta=dfracpi2-psi$ and use math.stackexchange.com/questions/1833153/… or math.stackexchange.com/questions/2021356/…
$endgroup$
– lab bhattacharjee
2 hours ago
$begingroup$
Set $theta=dfracpi2-psi$ and use math.stackexchange.com/questions/1833153/… or math.stackexchange.com/questions/2021356/…
$endgroup$
– lab bhattacharjee
2 hours ago
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$$(i).a=sin(theta)+cos(phi)$$
$$(ii).b=cos(theta)+sin(phi)$$
$$(i)^2+(ii)^2=2+2sin(theta +phi)$$so
$$sin(theta+phi) ={(a^2+b^2)over 2}-1$$.
$$(i)*(ii)={sin(2theta)+sin(2phi) over 2}+cos(theta-phi)=sin(theta+phi)cos(theta-phi)+cos(theta-phi)$$
so$$cos(theta-phi)={abover 1+sin(theta+phi)}={2abover a^2+b^2}$$
answered 3 hours ago
StAKmodStAKmod
406110
$endgroup$
$begingroup$
Wow, thank you, you've made it seem so simple. Was the path intuitive or how did you decide to choose this path?
$endgroup$
– Avinash Shastri
3 hours ago
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Avinash Shastri is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3152200%2fhelp-prove-this-basic-trig-identity-please%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$$(i).a=sin(theta)+cos(phi)$$
$$(ii).b=cos(theta)+sin(phi)$$
$$(i)^2+(ii)^2=2+2sin(theta +phi)$$so
$$sin(theta+phi) ={(a^2+b^2)over 2}-1$$.
$$(i)*(ii)={sin(2theta)+sin(2phi) over 2}+cos(theta-phi)=sin(theta+phi)cos(theta-phi)+cos(theta-phi)$$
so$$cos(theta-phi)={abover 1+sin(theta+phi)}={2abover a^2+b^2}$$
answered 3 hours ago
StAKmodStAKmod
406110
$endgroup$
$begingroup$
Wow, thank you, you've made it seem so simple. Was the path intuitive or how did you decide to choose this path?
$endgroup$
– Avinash Shastri
3 hours ago
add a comment |
$begingroup$
$$(i).a=sin(theta)+cos(phi)$$
$$(ii).b=cos(theta)+sin(phi)$$
$$(i)^2+(ii)^2=2+2sin(theta +phi)$$so
$$sin(theta+phi) ={(a^2+b^2)over 2}-1$$.
$$(i)*(ii)={sin(2theta)+sin(2phi) over 2}+cos(theta-phi)=sin(theta+phi)cos(theta-phi)+cos(theta-phi)$$
so$$cos(theta-phi)={abover 1+sin(theta+phi)}={2abover a^2+b^2}$$
answered 3 hours ago
StAKmodStAKmod
406110
$endgroup$
$begingroup$
Wow, thank you, you've made it seem so simple. Was the path intuitive or how did you decide to choose this path?
$endgroup$
– Avinash Shastri
3 hours ago
add a comment |
$begingroup$
$$(i).a=sin(theta)+cos(phi)$$
$$(ii).b=cos(theta)+sin(phi)$$
$$(i)^2+(ii)^2=2+2sin(theta +phi)$$so
$$sin(theta+phi) ={(a^2+b^2)over 2}-1$$.
$$(i)*(ii)={sin(2theta)+sin(2phi) over 2}+cos(theta-phi)=sin(theta+phi)cos(theta-phi)+cos(theta-phi)$$
so$$cos(theta-phi)={abover 1+sin(theta+phi)}={2abover a^2+b^2}$$
answered 3 hours ago
StAKmodStAKmod
406110
$endgroup$
$$(i).a=sin(theta)+cos(phi)$$
$$(ii).b=cos(theta)+sin(phi)$$
$$(i)^2+(ii)^2=2+2sin(theta +phi)$$so
$$sin(theta+phi) ={(a^2+b^2)over 2}-1$$.
$$(i)*(ii)={sin(2theta)+sin(2phi) over 2}+cos(theta-phi)=sin(theta+phi)cos(theta-phi)+cos(theta-phi)$$
so$$cos(theta-phi)={abover 1+sin(theta+phi)}={2abover a^2+b^2}$$
answered 3 hours ago
StAKmodStAKmod
406110
answered 3 hours ago
StAKmodStAKmod
406110
answered 3 hours ago
StAKmodStAKmod
406110
answered 3 hours ago
StAKmodStAKmod
406110
406110
$begingroup$
Wow, thank you, you've made it seem so simple. Was the path intuitive or how did you decide to choose this path?
$endgroup$
– Avinash Shastri
3 hours ago
add a comment |
$begingroup$
Wow, thank you, you've made it seem so simple. Was the path intuitive or how did you decide to choose this path?
$endgroup$
– Avinash Shastri
3 hours ago
$begingroup$
Wow, thank you, you've made it seem so simple. Was the path intuitive or how did you decide to choose this path?
$endgroup$
– Avinash Shastri
3 hours ago
$begingroup$
Wow, thank you, you've made it seem so simple. Was the path intuitive or how did you decide to choose this path?
$endgroup$
– Avinash Shastri
3 hours ago
add a comment |
Avinash Shastri is a new contributor. Be nice, and check out our Code of Conduct.
Avinash Shastri is a new contributor. Be nice, and check out our Code of Conduct.
Avinash Shastri is a new contributor. Be nice, and check out our Code of Conduct.
Avinash Shastri is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3152200%2fhelp-prove-this-basic-trig-identity-please%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
$begingroup$
Welcome to Math Stack Exchange. Do you know the formula for cosine of a difference?
$endgroup$
– J. W. Tanner
4 hours ago
$begingroup$
Yes, $cos(theta-phi)=cos(theta)cos(phi)+sin(theta)sin(phi)$, and I went much further but was not able to poduce anything useful in the sense of the proof.
$endgroup$
– Avinash Shastri
4 hours ago
$begingroup$
Set $theta=dfracpi2-psi$ and use math.stackexchange.com/questions/1833153/… or math.stackexchange.com/questions/2021356/…
$endgroup$
– lab bhattacharjee
2 hours ago