verify the identity of sin^2(x)=1/2(1-cos2x)

Question

I have to verify the identity. I know I need to start with the right side, but am completely lost. Help please!

Answer 1

We know that cos2x =cos^2x-sin^2x

Right hand side

= 1/2(1-cos2x)

= 1/2[1-(cos^2(x)-sin^2(x))]

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

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

= 1/2(2sin^2(x))

= sin^2(x)

= Left hand side.