Решить уравнение

5sin^2 (5x) - 0.5 sin 10x - 3 cos^2 (5x) = 3

5sin^2 (5x) - 0.5 sin 10x - 3 cos^2 (5x) = 3

5sin^2 (5x) - sin 5xcos5x - 3 cos^2 (5x) = 3sin^2 (5x) + 3 cos^2 (5x)

2sin^2 (5x) - sin 5xcos5x - 6 cos^2 (5x) = 0

2tg^2 (5x) - tg (5x) - 6=0

d=1+4*6*2=49

tg (5x) = (1+7) / 4 или tg (5x) = (1-7) / 4

tg (5x) = 2 или tg (5x) = - 1,5

5 х=arctg (2) + pi*k или 5 х=-arctg (1,5) + pi*k

х=arctg (2) / 5+pi*k/5 или х=-arctg (1,5) / 5+pi*k/5