prove that (sin^4x-cos^4x)/(sinx-cosx) = sinx+cosx

Answer 1

(sin^4x-cos^4x)/(sinx-cosx)
=(sin^2x+cos^2x)(sin^2x-cos^2x)/(sinx-cosx)
=1*(sinx+cosx)(sinx-cosx)/(sinx-cosx)
=sinx+cosx