Answer:
[tex]\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)[/tex]
Step-by-step explanation:
We want to simplify:
[tex]\displaystyle \frac{\cos^2(A)}{1+\sin(A)}[/tex]
Recall the Pythagorean Identity:
[tex]\sin^2(A)+\cos^2(A)=1[/tex]
So:
[tex]\cos^2(A)=1-\sin^2(A)[/tex]
Substitute:
[tex]\displaystyle =\frac{1-\sin^2(A)}{1+\sin(A)}[/tex]
Factor. We can use the difference of two squares pattern:
[tex]\displaystyle =\frac{\left(1-\sin(A))(1+\sin(A))}{1+\sin(A)}[/tex]
Cancel. Hence:
[tex]\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)[/tex]
