simplify the trigonometric expression. cos^2θ/1-sinθ

Answer 1

To simplify the trigonometric expression cos^2θ / (1 - sinθ), we can first use the Pythagorean identity cos^2θ = 1 - sin^2θ.

Substitute cos^2θ = 1 - sin^2θ into the expression:
(1 - sin^2θ) / (1 - sinθ)

Now, we can factor out a negative sign from the numerator:
-(sin^2θ - 1) / (1 - sinθ)

Next, we can factor out a negative sign from the numerator, and factor out a negative sign from the denominator:
(sin^2θ - 1) / (sinθ - 1)

Therefore, the simplified expression of cos^2θ / (1 - sinθ) is (sin^2θ - 1) / (sinθ - 1).