95. Ифодахоро сода кунед: а) \(\frac{\sin 4\alpha}{\cos 2\alpha}\); б) \(\frac{\cos 2\alpha}{\cos\alpha-\sin\alpha}-\cos\alpha\); в) \(\cos 2\beta+\sin^2\beta\).

а) \(\frac{\sin4\alpha}{\cos2\alpha}=\frac{2\sin2\alpha\cos2\alpha}{\cos2\alpha}=2\sin2\alpha\).

б) \(\frac{\cos2\alpha}{\cos\alpha-\sin\alpha}-\cos\alpha=\frac{(\cos\alpha-\sin\alpha)(\cos\alpha+\sin\alpha)}{\cos\alpha-\sin\alpha}-\cos\alpha=\sin\alpha\).

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

Ответ: а) \(2\sin2\alpha\); б) \(\sin\alpha\); в) \(\cos^2\beta\).