Question

Решить уравнение!!!!

Answer 1

$3 {sin}^{2} x + sinx times cosx = 2 {cos}^{2} x \ 3 {sin}^{2} x + sinx times cosx - 2 {cos}^{2} x = 0 \ frac{3 {sin}^{2} x}{ {cos}^{2}x } + frac{sinx times cosx}{ {cos}^{2}x } - frac{2 {cos}^{2} x}{ {cos}^{2}x } = 0 \ 3 {tg}^{2} x + tgx - 2 = 0 \ tgx = t \ 3 {t}^{2} + t - 2 = 0 \ d = {b}^{2} - 4ac = 1 - 4 times 3 times ( - 2) = 25 \ x1 = frac{ - 1 + 5}{2 times 3} = frac{4}{6} = frac{2}{3} \ x2 = frac{ - 1 - 5}{2 times 3} = frac{ - 6}{6} = - 1 \ 1)tgx = frac{2}{3} \ x = arctg frac{2}{3} + pi n \ 2)tgx = - 1 \ x = arctg( - 1) + pi n \ x = - frac{pi}{4} + pi n$
Ответ:
arctg2/3 + pi*n, n € Z;
-pi/4 + pi*n, n € Z.