prove the following trigonometric identity : sin^2 (theta) + 2 sin (theta)cos (theta) = 1- cos^2 (theta) + sin 2(theta)

Question

Note that the left and right side are simplified separately

Answer 1

sin^2x +2simxcosx =1-cos^2x+2in2x

sin^2x + cos^2x = 1      , sin^2x = 1 - cos^2x  and 2sinxcosx = sin2x

1 - cos^2x + sin2x = 1-cos^2x + sin2x