I am having a problem verifying this trigonometric identity. Sin^2-Sin^4=Cos^2-Cos^4. Can someone please help?

Answer 1

LHS=sin^2x-sin^4x
=sin^2x(1-sin^2x)
=sin^2xcos^2x
=(1-cos^2x)(cos^2x)
=cos^2x-cos^4x
=RHS
hence proved

Answer 2

Remember that sin^2 + cos^2 = 1
So 1- sin^2 x = cos^2 and 1 - cos^2 = sin^2 x

sin^2 x - sin^4 x = cos^2 x - cos^4 x

sin^2x (1 - sin^2 x) = cos^2 x (1 - cos^2 x)

Just substitute and thats it!

Ana