Verify \(cos \ 90^{\circ} = 1 - 2 \ sin^2 \ 45^{\circ} = 2 \ cos^2 \ 45^{\circ} - 1\)
Proof:
\(cos \ 90^{\circ} =\)
\(1 - 2 \ sin^2 \ 45^{\circ} =\)
\(2 \ cos^2 \ 45^{\circ} - 1 =\)
Thus, \(cos \ 90^{\circ} = 1 - 2 \ sin^2 \ 45^{\circ} = 2 \ cos^2 \ 45^{\circ} - 1\).
Hence, we proved.