Cos^2 (5x) + 7sin^2 (5x) = 8 sin5x cos5x

cos² 5x + 7sin² 5x - 8sin5x cos5x = 0

cos² 5x cos² 5x cos² 5x cos² 5x

1 + 7tg² 5x - 8tg 5x = 0

Замена tg 5x = y

7y² - 8y + 1=0

D=64 - 28 = 36

y₁ = 8-6 = 2/14 = 1/7

14

y₂ = 8+6 = 1

14

При у = 1/7

tg 5x=1/7

5x = arctg 1/7 + πk, k∈Z

x = 0.2 arctg1/7 + 0.2πk, k∈Z

При у=1

tg 5x=1

5x = π/4 + πk, k∈Z

x = π/20 + 0.2πk, k∈Z

Ответ: 0,2arctg 1/7 + 0.2πk, k∈Z;

π/20 + 0.2πk, k∈Z