Answer
$(sinx+cosx)^{2}=1+sin2x$
Work Step by Step
Need to prove the identity $(sinx+cosx)^{2}=1+sin2x$
In order to prove this, take left side isolate.
$(sinx+cosx)^{2}=sin^{2}x+cos^{2}x+2sinx cosx$
Since, $2sinx cosx= sin2x$, and $sin^{2}x+cos^{2}x=1$
Hence, $(sinx+cosx)^{2}=1+sin2x$
