Trigonometric identity Definition and 85 Threads

Homework Statement cos(x-y)cosy-sin(x-y)siny=cosx a.try to prove that the equation is an identity b. determine a counterexample to show that it is not an identity Homework Equations cos(x-y) = cosxcosy+sinxsiny sin(x-y) = sinxcosy-cosxsiny The Attempt at a Solution a.Left side of...

Could anyone please tell me how are those two expressions equivalent?! what are the identities used?

Homework Statement http://img829.imageshack.us/img829/3413/daumequation13237287425.png Prove that LS=RS. Homework Equations There are no relevant equations. The Attempt at a Solution http://img829.imageshack.us/img829/3413/daumequation13237287425.png

Hi, I am trying to figure out what the result is when adding two sinusoids of the same frequency but with different phase and amplitudes. Specifically I want to know if the result is always another sinusoid of the same frequency. For the case of the the same amplitude I have: cos(wt) +...

In the following question I figure that i need to prove that h holds true with the trigonometric identity subbed into the denominator. I'm not sure how to simplify the equation any further after that though. Can someone provide any insight...

Homework Statement cos\theta/1-tan\theta+sin\theta/1-cot\theta=sin\theta+cos\theta Homework Equations The Attempt at a Solution

Homework Statement \cos (\frac{(-1)\pi x}{L})-\cos (\frac{3\pi x}{L}) Homework Equations The Attempt at a Solution the first cosine is the same as positive but is the second cosine simply equal to \cos (\frac{\pi x}{L})? thanks!

I'm reading through a solution to a problem and at one point the following identity is used: \frac{1-\cos(\beta)}{\sin(\beta)}=\frac{\sin(\frac{\beta}{2})}{\cos(\frac{\beta}{2})} I've been trying to figure out where this comes from but with haven't got it yet. Any ideas?

Hey guys. How are you all doing? I'm helping my younger brother out with his trigonometry homework. He is dealing with verifying trigonometric identities. However, he has the problem that I am getting nowhere with. Hope you all can help. Thanks in advance. :) Homework Statement Verify...

Hello, Could you please clarify if this is correct: If tan^(-1)(x) = Pi/2 - tan^(-1)(1/x) Then if we have (ax) as the angle where a is a constant, do we get: tan^(-1)(ax) = Pi/2 - tan^(-1)(a/x) or does the constant go on the bottom with the x? i.e. or: tan^(-1)(ax) = Pi/2 -...

Homework Statement prove that: tan(1+cos(x))^2 = 1-cos(x) Homework Equations trig identities, like the pythagorean, sum/difference, double/half angle identities, power reducing identities, etc... The Attempt at a Solution i'm not sure where to start; i tried using the pythagorean...

Hi I've got this problem which has really been bothering me. How are you supposed to prove that: (Sin[A] Sin[2 A] + Sin[3 A] Sin[6 A])/(Sin[A] Cos[2 A] + Sin[3 A] Cos[6 A]) is identicle to tan[5A]. I am almost sure that I've got to use the factor formulae, but I've had no luck. Maybe...

I'm looking over the differential equation describing a hanging cable in a textbook, and I probably need to review my trigonometric derivatives and integrals again because I'm not seeing how they got the following: \frac{dy}{dx} = tan(\phi) \frac{ws}{T_0} \frac{d^2y}{dx^2} =...

Hi Everyone, Do there exist any explicit formula for Cos(x_1+x_2+...+x_n) as a sum of products of Sin(x_i) & Cos(x_i)? Or we need to expand using Cos(A+B), Sin(A+B) again & again? If it exists then what is about Sin(x_1+x_2+...+x_n)? [It is understood that there will be 2^(n-1) number of...

Why is cos^2 x = \frac{1}{2} + \frac{cos(2x)}{2} ?

Homework Statement tanX+tan Y / 1-tanXtanY= cotX+cotY/cotXcotY-1 Homework Equations tan= sin/cos cot= cos/sin The Attempt at a Solution

Homework Statement verify the identity : 1+sec(-∅)/sin(-∅+tan(-∅) = -csc ∅ Homework Equations The Attempt at a Solution 1+sec∅/-sin-tan∅ = -csc∅ I don't know where to start from, does anyone have any idea?

cosx/1-sinx + 1-sinx/cosx = 2secx + 2tanx I can get to 2secx + tanx - tanx, any help is appreciated

[SOLVED] A Trigonometric Identity Probelm If I have sin^2 2x would I be able to apply the identity sin^2x = (1/2)(1-cos2x) to get this: sin^2 2x = 2(1/2)(1 - cos^2 x) Similarly, if I had sin^2 2x + cos^2 2x would I be able to use the identity sin^2 x + cos^2 x = 1 to get: sin^2 2x +...

Homework Statement find arc length of the segment of the 2space curbe that is defined by the parametric equations x(t) = t-sin(t) y(t) = 1+cos(t) 0 ≤ t ≤ 4π The Attempt at a Solution I've found dx/dt and dy/dt respectively and put them into the arc length equation, i.e...

Homework Statement http://img206.imageshack.us/img206/9099/titleol2.jpg http://g.imageshack.us/g.php?h=206&i=titleol2.jpg Show the above statement is equivalent to : sec (2x) + tan (2x) Homework Equations The Attempt at a Solution First attempt in which I used the...

Homework Statement Verify the possibility of an identity graphically. (Completed this part) Then, prove each identity algebraically. \dfrac{sinx+tanx}{cosx+1}=tanx Homework Equations tan\theta=\dfrac{sin\theta}{cos\theta} cot\theta=\dfrac{cos\theta}{sin\theta}...

Homework Statement I'm attempting to prove that 1 - sin^2 t /(1 + cos t) - cos^2/(1+tan t) = cos t sin t 2. The attempt at a solution I've tried various approaches. The most promising has the LHS reduced to: (sin t cos t (1 + cos t + sin t cos t))/((1 + cos t)(cos t + sin t))...

Im supposed to verify that (1-sinx)/(1+sinx) = (secx-tanx)^2 RHS = (secx-tanx)^2 = (1/cosx - sinx/cosx)^2 = [(1-sinx) / cosx]^2 = [(1-sinx)(1-sinx)]/cosx^2 = (1-2sinx+sinx^2)/(1-sinx^2) From here, I'm feeling pretty confused. I'm not even sure if all my values are correct.

Help with a Trigonometric identity... Homework Statement (sin x + sin 2x + sin 4x) / (cos x + cos 2x + cos 4x) = tan 2x Homework Equations sin 2x = 2sinxcosx; cos 2x = cos^2x - sin^2x The Attempt at a Solution solving left side, =[sin x + sin 2x + sin (2x + 2x)]/[cos x + cos...

For a homework assignment I'm supposed to prove that sin(x)^2+cos(x)^2=1, using only the following identities (along with algebraic operations): sin(-x)=-sin(x) cos(-x)=cos(x) cos(x+y)=cos(x)cos(y)-sin(x)sin(y) sin(x+y)=sin(x)cos(y)+cos(x)sin(y) I can't figure this out, because as far...

Which trigonometric identitiy are used to transform 2(cos(x))^2+2cos(x)sin(x) into 0?

Homework Statement http://www.jyu.fi/kastdk/olympiads/2004/Theoretical%20Question%203.pdf http://www.jyu.fi/kastdk/olympiads/2004/Solution%203.pdf Question A- (b) They use some trigomentric identity that I don't understand, which one is it? Thanks in advance. Homework...

Homework Statement Prove the following identity: (1 + cos \theta)^2 + sin^2\theta = 2(1 + cos \theta) Homework Equations cos^2 \theta + sin^2 \theta = 1 The Attempt at a Solution I've squared out the first bracket so that it becomes 1 + cos^2 \theta and multiplied out the second bracket so...

Hi. I need to prove the following identity \arccos{z} =i \ln { z + (z^2 -1)^\frac{1}{2} } I was given a hint to write \cos{A}=z, then rewrite \cos{A} in terms of the exponential. \cos{A}=\frac{\exp{iA}+\exp{-iA}}{2}=z I took the log on both sides and got stuck at that...

In my book, (cos4x)^2 is written 1+cos8x without referring to any formula. Which trig. identity is used here?

Can anyone help me solve the following problems? sec theta -1/1-cos theta = sec theta tan (pie/2 - theta) tan theta =1 Thanks

Hi, I have a question about a problem: 1/2csc(THETA)sec(THETA) I have to find the identity for it and I know that csc is 1/sin and sec is 1/cos but after that I don't see where it can lead to a simple answer. If anyone knows it would be helpful, thanks!

Trigonometric Identity?? I just can't figure this out. I don't think I've covered enough material to do this. Can anyone help? I've put the entire question but I am sure all i need is a little explanation and maybe the first answer and i could do the rest. :confused: Let z =...

Using the fact that z=e^ibeta and the identity 1 + z + z^2...+z^n=1-z^(n+1)/1-z Help me derive 1 + cosbeta +cos2beta + ... +cosnbeta= 1/2 + sin((2n+1)beta/2)/2sin(beta/2) where beta is between 0 and 2pi