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jenyasd209 [6]
2 years ago
5

Simplify cos^2 A/1+sin A

Mathematics
1 answer:
Stels [109]2 years ago
7 0

Answer:

\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)

Step-by-step explanation:

We want to simplify:

\displaystyle \frac{\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 =\frac{1-\sin^2(A)}{1+\sin(A)}

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

\displaystyle =\frac{\left(1-\sin(A))(1+\sin(A))}{1+\sin(A)}

Cancel. Hence:

\displaystyle \frac{\cos^2(A)}{1+\sin(A)}=1-\sin(A)

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