sin²x+sinx*cosx=0

Solve sin²x + sinx cosx = 0.

• Factor: sinx (sinx + cosx) = 0.

Thus the solutions come from:

1. sinx = 0 → x = kπ, k ∈ Z.
2. sinx + cosx = 0 → sinx = -cosx → tanx = -1 (cosx ≠ 0) → x = -π/4 + kπ, k ∈ Z. (Equivalent form: x = 3π/4 + kπ)

General solution: x = kπ or x = -π/4 + kπ, for any integer k.

If you want solutions in [0, 2π): x = 0, π, 3π/4, 7π/4.