Question

Simplify cos^2 A/1+sin A

Answer 1

`\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)`