How do you verify?

Question

8sin^2xcos^x=1-cos4x

Answer 1

LHS

8sin^2xcos^x =2(4sin^2xcos^x)

                      =2(sinxcosx)^2

                       =2sin^2(2x)

RHS

1-cos4x=1-(cos^2(2x)-sin^2(2x))

             =1-cos^2(2x)+sin^2(2x)

             =sin^2(2x)+sin^2(2x)

             =2sin^2(2x)

LHS =RHS

Hence, proved