Question

Sin²x-4sin x×cos x+3 cos² x=0

Answer 1

Ответ:

$x_1 = frac{pi}{4} + pi k; x_2= arctan (frac{1}{3} ) + pi k, k in mathbb {Z}$

Пошаговое объяснение:

$sin ^2 x - 4sin x cos x + 3 cos^2 x = 0 | : sin^2 x neq 0; x neq pi k, k in mathbb {Z}\ 1 - 4tan x + 3tan^2 x = 0\3tan^2 x - 4tan x + 1 = 0 |  t = tan x\3t^2-4t+1=0\t_1=1 ; t_2 = frac{1}{3} \tan x = 1 tan x = frac{1}{3}\x_1 = frac{pi}{4} + pi k; x_2= arctan (frac{1}{3} ) + pi k, k in mathbb {Z}$