3sin^2x + cos^2x=5cosx

3sin^2 (x) + cos^2 (x) = 5cosx;

3 (1 - cos^2 (x)) + cos^2 (x) - 5cos (x) = 0;

3 - 2cos^2 (x) - 5cos (x) = 0;

2cos^2 (x) + 5cos (x) - 3 = 0;

Сделаем замену переменной: cos (x) = t.

2t^2 + 5t - 3 = 0;

D = 49;

t1 = - 3; не удовлетворяет условиям.

t2 = 1/2;

cos (x) = 1/2;

x = ±п/3 + 2 пk, k∈Z.

Ответ: x = ±п/3 + 2 пk, k∈Z.