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

A)
LS
= cos^4(x) -sin^4(x)
= (cos^2(x) - sin^2(x)) (cos^2(x) + sin^2(x))
= (cos (2x)) (1)
= cos (2x)
= RS

B)
There must be a typo in your second problem. If you plug an actual angle into it, LS is not equal to RS.