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.