Question

16.Решить уравнение

Answer 1

$3 { sin}^{2} x + sinxcosx = 2cos ^{2} x : : : |: {cos}^{2} x, : cosx neq 0 \ \ 3tg ^{2} x + tgx = 2 \ 3tg ^{2} x + tgx - 2 = 0 \ D = 1 + 4 times 2 times 3 = 1 + 24 = 25 = {5}^{2} \1)tgx = frac{ - 1 + 5}{2 times 3} = frac{4}{6} = frac{2}{3} \ \ x = arctg frac{2}{3} + pi n, : n in Z \ \ 2)tgx = frac{ - 1 - 5}{2 times 3} = frac{ - 6}{6} =- 1 \ \ x = - frac{pi}{4} + pi n, : n in Z \ \ OTBET:arctg frac{2}{3} + pi n ; : frac{pi}{4} + pi n, : n in Z$