Question

Нужно упростить
1/(cos^2a-sin^2a+sin2a*tg2a)

Answer 1

$\frac{1}{cos^2a-sin^2a+sin2a\cdot tg2a}=\frac{1}{cos2a+sin2a\cdot \frac{sin2a}{cos2a}}=\frac{cos2a}{cos^22a+sin^22a}=\frac{cos2a}{1}=cos2a$

Answer 2

$\dfrac{1}{\cos^2\alpha-\sin^2\alpha+\sin2\alpha\cdot {\rm tg}2\alpha}=\dfrac{1}{\cos 2\alpha+\sin2\alpha \cdot \dfrac{\sin2\alpha}{\cos2\alpha}}=\\ \\ \\ =\dfrac{\cos2\alpha}{\cos^22\alpha+\sin^22\alpha}=\dfrac{\cos2\alpha}{1}=\cos2\alpha$