7. cera(1-cos2x)+cos² a;

7. $$ctg^2 \alpha(1 - \cos 2\alpha) + \cos^2 \alpha = ctg^2 \alpha (1 - (\cos^2 \alpha - \sin^2 \alpha)) + \cos^2 \alpha = ctg^2 \alpha (1 - \cos^2 \alpha + \sin^2 \alpha) + \cos^2 \alpha = ctg^2 \alpha (2\sin^2 \alpha) + \cos^2 \alpha = \frac{\cos^2 \alpha}{\sin^2 \alpha} \cdot 2\sin^2 \alpha + \cos^2 \alpha = 2\cos^2 \alpha + \cos^2 \alpha = 3\cos^2 \alpha$$

Ответ: $$3\cos^2 \alpha$$