1sin²x+5*sinx-6=0

Solve sin^2 x + 5 sin x − 6 = 0. - Let t = sin x. Then t^2 + 5t − 6 = 0. - Factor: (t + 6)(t − 1) = 0 → t = 1 or t = −6. - Since |sin x| ≤ 1, t = −6 is impossible. So sin x = 1. General solution: - x = π/2 + 2kπ, where k ∈ Z. If you want solutions in [0, 2π): - x = π/2.