Step 1

\(\cos(2x)=\cos(x+x)\)

\(=\cos(x)\cos(x)-\sin(x)\sin(x)\)

Since \(\cos(A+B)=\cos A\cos B-\sin A\sin B\)]

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

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

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

\(=1-1\)

\(=0\)