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