Rewrite with only sin x and cos x.

sin 2x - cos 2x

Given:

sin2x-cos2x

now by applying double angle formula

for sin2x

sin2x = 2sinx*cosx

for cos2x

cos2x = (cosx*cosx - sinx*sinx)

now putting these above values in given equation

2sinx*cosx - (cosx*cosx - sinx*sinx)

now simplifyng

2sinx*cosx - cosx*cosx + sinx*sinx

so the right answer is

2sinx*cosx - cosx*cosx + sinx*sinx