Answer
$(sinx+cosx)^{2}=1+sin2x$
Work Step by Step
We need to prove the identity $(sinx+cosx)^{2}=1+sin2x$
We have:
$(sinx+cosx)^{2}=sin^{2}x+cos^{2}x+2sinx cosx$
Also, $2sinx cosx= sin2x$, and $sin^{2}x+cos^{2}x=1$
Hence, $(sinx+cosx)^{2}=1+sin2x$
