veify that each equation is an identity

Question

cos2x+tan2xcos2x=1

sin4x-cos4x/sin2x=1-cot2x

Answer 1

Does cos2x mean cosine squared? cos^2(x)

If so, then you have

cos^2(x) + sin^2(x)/cos^2(x) * cos^2(x)
= cos^2(x) + sin^2(x)
= 1

If you mean cos(2x) then the equation is not an identity (e.g.: x = pi/2)