Question

3sin^2(x)-4sin(x)cos(x)+cos^2(x)=0

Answer 1

$3 {sin}^{2} x - 4sinxcosx + {cos}^{2} x = 0 \ frac{3 {sin}^{2} x}{ {cos}^{2} x} - frac{4sinxcosx}{ {cos}^{2}x } + frac{ {cos}^{2} x}{ {cos}^{2}x } = 0 \ 3 {tg}^{2} x - 4tgx + 1 = 0 \ tgx = t \ 3 {t}^{2} - 4t + 1 = 0 \ d = {b}^{2} - 4ac = 16 - 4 times 3 = 16 - 12 = 4 \ t1 = frac{4 + 2}{2 times 3} = frac{6}{6} = 1 \ t2 = frac{ 4 - 2}{2 times 3} = frac{2}{6} = frac{1}{3} \ 1)tgx = 1 \ x = frac{pi}{4} + pi n \ 2)tgx = frac{1}{3} \ x = arctg frac{1}{3} + pi n$
Ответ: p/4 + pi*n, n € Z; arctg1/3 + pi*n, n € Z.