Question

известно, что $frac{sin a + 3 cos a}{sin a - cos a}$ = 3 чему равна cos2a

Answer 1

$frac{ sin(a) + 3 cos(a) }{ sin(a) - cos(a) } = 3 \ \ 3(sin(a) - cos(a)) = sin(a) + 3 cos(a) \ \ 3 sin(a) - 3 cos(a) = sin(a) + 3 cos(a) \ \ 2 sin(a) - 6 cos(a) = 0 \ \ sin(a) - 3 cos(a) = 0$
Разделим на соsa : cosa ≠ 0

$tga - 3 = 0 \ tga = 3$

Воспользуемся формулой:

${(tga)}^{2} + 1 = frac{1}{ { (cos(a)) }^{2} } \ \ frac{1}{ { (cos(a)) }^{2} } = 10 \ \ { (cos(a) )}^{2} = frac{1}{10}$

$cos(2a) = 2 { (cos(a) )}^{2} - 1 = 2 times frac{1}{10} - 1 = \ \ = frac{1}{5} - 1 = 0.2 - 1 = - 0.8$


ОТВЕТ: -0,8