4 в степени cos2x + 4 в степени cos^2 x = 3

4^ (cos (2x)) + 4^ (cos^2 (x)) = 3

cos (2x) = 2cos^2 (x) - 1

0.25*4^ (2cos^2 (x)) + 4^ (cos^2 (x)) - 3 = 0

Замена: 4^ (cos^2 (x)) = t > 1

0.25*t^2 + t - 3 = 0

t^2 + 4t - 12 = 0, D=64,

t1 = - 6 < 0 - посторонний корень

t2 = 2

4^ (cos^2 (x)) = 2

2^ (2cos^2 (x)) = 2

2cos^2 (x) = 1, cos^2 (x) = 1/2

cosx = √2/2, x = + - π/4 + 2πk

cosx = - √2/2, x = + - 3π/4 + 2πk

Объединяем: x = + - π/4 + πk/2

Ответ: x = + - π/4 + πk/2