Trigonometric Identities Proof

[whitehorsey]

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!

 

[rock.freak667]

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.

 

[Bohrok]

(B) cos(-x) = - cos x
needs to be cos(-x) = cos x without the minus in front on the right side.