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)
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