Решение
2sin²x-7cos2x=6sin2x+7
- 7 - 7cos2x + 2sin²x - 6sin2x = 0
- 2*(3 + 4cos2x + 3sin2x) = 0
3 + 4cos2x + 3sin2x = 0
3sin²x + 3cos²x + 4cos²x - 4sin²x + 6sinx*cosx = 0
7cos²x - sin²x + 6sinxcosx = 0 делим на (- cos²x) ≠ 0
tg²x - 6tgx - 7 = 0
1) tgx = - 1
x₁ = - π/4 + πk, k ∈ Z
2) tgx = 7
x₂ = arctg7 + πn, n ∈ Z