## Calculus 8th Edition

$(sinx+cosx)^{2}=1+sin2x$
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, $(sinx+cosx)^{2}=1+sin2x$