Simplify cos^2 A/1+sin A

Question

asked Oct 3, 2022 106k views

1 Answer

Russ Jackson · Answer 1 · 2022-10-09T02:29:06+0000

Answer:

$\displaystyle (\cos^2(A))/(1+\sin(A))=1-\sin(A)$

Explanation:

We want to simplify:

$\displaystyle (\cos^2(A))/(1+\sin(A))$

Recall the Pythagorean Identity:

$\sin^2(A)+\cos^2(A)=1$

So:

$\cos^2(A)=1-\sin^2(A)$

Substitute:

$\displaystyle =(1-\sin^2(A))/(1+\sin(A))$

Factor. We can use the difference of two squares pattern:

$\displaystyle =(\left(1-\sin(A))(1+\sin(A)))/(1+\sin(A))$

Cancel. Hence:

$\displaystyle (\cos^2(A))/(1+\sin(A))=1-\sin(A)$