Question

Вычислите cos2a если tga=-7

Answer 1

Ответ:

$\cos(2 \alpha ) = 2\cos {}^{2} ( \alpha ) - 1$

найдем cos^2(a) по формуле:

$1 + {tg}^{2} \alpha = \frac{1}{ \cos {}^{2} ( \alpha ) } \\ \cos {}^{2} ( \alpha ) = \frac{1}{1 + {tg}^{2} \alpha }$

$tg \alpha = - 7$

$\cos {}^{2} ( \alpha ) = \frac{1}{1 + 49} = \frac{1}{50} \\ \\ \cos(2 \alpha ) = 2 \times \frac{1}{50} - 1 = \frac{1}{25} - 1 = \\ = 0.04 - 1 = - 0.96$