4 в степени cos2x+4 в степени cos2x=3

4^(cos(2x)) + 4^(cos^2(x)) = 3cos(2x) = 2cos^2(x) - 10.25*4^(2cos^2(x)) + 4^(cos^2(x)) - 3 = 0Замена: 4^(cos^2(x)) = t > 10.25*t^2 + t - 3 = 0t^2 + 4t - 12 = 0, D=64,t1 = -6 < 0 - посторонний кореньt2 = 24^(cos^2(x)) = 22^(2cos^2(x)) = 22cos^2(x) = 1, cos^2(x) = 1/2cosx = √2/2, x = +-π/4 + 2πkcosx = -√2/2, x = +-3π/4 + 2πkОбъединяем: x = +-π/4 + πk/2Ответ: x = +-π/4 + πk/2