Question

Anybody know the answer to this?

Answer 1

I recognize that as the cosine double angle formula. The cosine sum angle formula is

$\cos (a+b) = \cos a \cos b - \sin a \sin b$

Setting a=b

$\cos(2a) = \cos^2 a - \sin^2 a$

Substituting $\cos^2 a = 1- \sin^2 a$

$\cos(2a) = 1 - \sin ^2 a - \sin^2a = 1 - 2 \sin^2 a$

Setting a=x/2,

$\cos x = 1 - \sin ^2 \frac x 2$

Answer: cos