Prove the following: cos(3π/4 + x) - cos(3π/4 - x) = -√2sinx

LHS=cos(3π/4+x) - cos(3π/4 - x) = cos(3π/4)cosx - sin(3π/4)sinx - [cos(3π/4)cosx + sin(3π/4)sinx] = -2sin(3π/4)sinx = -√2sinx = RHS ∴L.H.S=R.H.S ∴cos(3π/4+x) - cos(3π/4 - x) = -√2sinx Hence, proved