Question

решить
$8 sin x - 1 = 4 cos^{2} x$

Answer 1

$8 sin(x) - 1 = 4(1 - { sin(x) }^{2}) \ sin(x) = t \ 8t - 1 = 4 - 4 {t}^{2} \ 4 {t}^{2} + 8t - 5 = 0 \ d = 64 - 4 times 4 times ( - 5) = 64 + 80 = 144 \ t1 = frac{ - 8 - 12}{8} = - frac{5}{2} \ t2 = frac{ - 8+ 12}{8} = frac{4}{8} = frac{1}{2} \ sin(x) = - frac{5}{2} : : eto : newozmozhna : \ sin(x) = frac{1}{2} \ x = frac{pi}{6} + pi times k$