Using trigonometric identities, show that (cos(x) + sin(x))^2=1+sin(2x)

First being by expanding the brackets of the formula on the left:  (cos(x) + sin(x))² = (cos(x) + sin(x))*(cos(x) + sin(x)) = cos²(x)+2cos(x)sin(x)+sin²(x).Now we must use our understanding of trigonometric identities: remember that cos²(x)+sin²(x)=1 and 2cos(x)sin(x)=sin(2x).Substituting these identities back into the expanded form of the equation, we show that (cos(x) + sin(x))²=1+sin(2x)