cos^2 theta = 3(1-sin theta)

Answer 1

cos²θ = 3(1-sinθ)

From sin²θ + cos²θ = 1, cos²θ = 1 - sin²θ. Put this in cos²θ = 3(1-sinθ).

Now, 1 - sin²θ = 3 - 3sinθ.

Move everything to the right side, and we'll get sin²θ - 3sinθ + 2 = 0.

We can factor sin²θ - 3sinθ + 2 as (sinθ - 1)(sinθ - 2), so we have (sinθ - 1)(sinθ - 2) = 0.

Either sinθ = 1 or sinθ = 2. Because sinθ cannot be 2, it must be 1.

If your θ is between 0 and 2π, θ = π/2 because that's the only angle between 0 and 2π that satisfies sinθ = 1.