Question

Доказать тождество:
cos4a*tg2a-sin4a=-tg2a

Answer 1

$(\cos {4\alpha} + 1)\mathrm {tg} \: 2\alpha = \sin {4\alpha} \\ \\ \mathrm{tg} \: 2\alpha = \dfrac{\sin {4\alpha}}{\cos{4\alpha} + 1} = \dfrac{2\sin{2\alpha}\cos{2\alpha}}{2\cos^2{2\alpha} - 1 + 1} = \dfrac{\sin {2\alpha}}{\cos{2\alpha}}$