4) \(\cos 2\alpha+\sin^2\alpha\)

Применим формулу \(\cos2\alpha=1-2\sin^2\alpha\):

\(\cos2\alpha+\sin^2\alpha=1-2\sin^2\alpha+\sin^2\alpha=1-\sin^2\alpha=\cos^2\alpha\).

Ответ: \(\cos^2\alpha\).