Simplify sin x cos x2 sin 2xSolution sinx cosx2 sin2x P

Simplify

Solution

(sinx + cosx)^2 - sin2x =

Proof:
(sinx + cosx)^2 - sin2x

=sin^2(x) + 2sinx cosx + cos^2(x) - sin2x

By identity 1) (sinx + cosx)^2 = sin^2(x) + cos^2(x) +2sinx cosx

2) sin2x =2sinx cosx.

using the following identities,
sin^2(x) + cos^2(x) + 2sinx cosx - 2sinx cosx =1

Hence ,(sinx + cosx)^2 - sin2x = 1