Someone please help me prove these

Question

A) cos^4x-sin^4x=cos2x

B)tanx=sin^2x/1+cos^2x

Please and Thank you

Answer 1

looks like you need to review your basic identities and double-angle formulas:

cos^4x-sin^4x
= (cos^2x-sin^2x)(cos^2x+sin^2x)
= cos^2x-sin^2x
= cos2x

(B) is clearly not true, since sin^2x/(1+cos^2x) has no asymptotes