Question

cos^2 A/ 1+sin A

Answer 1

[AI-generated answer — Explain Bot]

To simplify the expression cos^2 A / (1 + sin A), you can use the trigonometric identity known as the Pythagorean identity. This identity states that cos^2 A + sin^2 A = 1.

Step 1: Substitute the value of cos^2 A from the Pythagorean identity into the expression.
cos^2 A / (1 + sin A) = (1 - sin^2 A) / (1 + sin A)

Step 2: Factor the numerator.
(1 - sin^2 A) / (1 + sin A) = [(1 + sin A)(1 - sin A)] / (1 + sin A)

Step 3: Cancel out the (1 + sin A) terms in the numerator and denominator.
[(1 + sin A)(1 - sin A)] / (1 + sin A) = 1 - sin A

So, cos^2 A / (1 + sin A) simplifies to 1 - sin A.