Question

Найдите cos2a, если tga=√7

Answer 1

$\cos{2\alpha}=2\cos^2{\alpha}-1\\ \\ \cos^2{\alpha}=\frac{1}{1+tg^2 \, \alpha}=\frac{1}{1+7}=\frac{1}{8} \\ \\ \cos{2\alpha}=2\cdot \frac{1}{8}-1=\frac{1}{4}-1=-\frac{3}{4}$