Question

Вычислить ctg^2(a) - tg^2(a), если cos 2a=1/4 Спасибо)

Answer 1

$ctg^2a-tg^2a=\frac{cos^2a}{sin^2a}-\frac{sin^2a}{cos^2a} \\\\ cos2a=cos^2a-sin^2a=0.25\\ 2cos^2a-1=0.25\\ cos^2a=\frac{1.25}{2}\\ sin^2a=1-\frac{1.25}{2}^2=\frac{2.4375}{2}\\ \\ ctg^2a-tg^2a=\frac{\frac{1.25}{2}}{\frac{2.4375}{2}}-\frac{\frac{2.4375}{2}}{\frac{1.25}{2}}=\\ \frac{1.25}{2.4375}-\frac{2.4375}{1.25}=-1.(5)$