Verify that \(\sin ^{2}(x)=\left(\frac{1}{2}\right)(1-\cos 2 x)\) [solved]

Question

Verify  that \(\sin ^{2}(x)=\left(\frac{1}{2}\right)(1-\cos 2 x)\)

Answer 1

\(\sin ^{2}(x)=\frac{1}{2}(1-\cos (2 x))\)

But \(\cos (2 x)=\cos ^{2}(x)-\sin ^{2}(x)\)

\(2 \sin ^{2}(x)=1-\cos ^{2}(x)+\sin ^{2}(x)\)
\(2 \sin ^{2}(x)-\sin ^{2}(x)=1-\cos ^{2}(x)\)  

But \(\sin ^{2}(x)+\cos ^{2}(x)=1\)
So: \(\sin ^{2}(x)=1-\cos ^{2}(x)\)
\(\sin ^{2}(x)=\sin ^{2}(x)\)