Trigonometric Identities Proof

AI Thread Summary
The discussion focuses on deriving trigonometric identities using fundamental equalities. Key identities include sin(-x) = -sin x and cos(-x) = cos x, which are essential for proving other equations. Participants express difficulty in deriving the absolute values of cos x/2 and sin x/2, seeking clarification on the process. Suggestions include setting A equal to B in the cosine addition formula and adjusting variables accordingly. The conversation emphasizes the importance of correctly applying trigonometric properties to achieve the desired results.
whitehorsey
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1. (A) sin(-x) = - sin x (C) cos(x+y) = cosxcosy - sinxsiny
(B) cos(-x) = - cos x (D) sin(x+y) = sinxcosy + cosxsiny
Use these equalities to derive the following trigonometric identities.
a. absolute value of cos x/2 = \sqrt{}1 + cosx/2
b. absolute value of sin x/2 = \sqrt{}1 - cosx/2


2.above



3. I'm stuck on these two and tried to think of different ways to solve it but I can't seem to get find a solution to it. Can you please explain how to derive those two equations? Thank You!
 
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cos(A+B) = cosAcosB - sinAsinB, try setting A=B and then see what happens. Since there is an x/2, maybe you should replace A with that.
 
(B) cos(-x) = - cos x
needs to be cos(-x) = cos x without the minus in front on the right side.
 

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