SOLUTION: Please help me with the following problem: If we extablish an identity: (cos^2 A)/(1 + sin A) would equal which of the following? 1. cos^2 A + cot A cos A 2. 1 + sin A 3. 1 -

Algebra ->  Trigonometry-basics -> SOLUTION: Please help me with the following problem: If we extablish an identity: (cos^2 A)/(1 + sin A) would equal which of the following? 1. cos^2 A + cot A cos A 2. 1 + sin A 3. 1 -       Log On


   



Question 150175: Please help me with the following problem:
If we extablish an identity:
(cos^2 A)/(1 + sin A) would equal which of the following?
1. cos^2 A + cot A cos A
2. 1 + sin A
3. 1 - sin A
4. 1
Thank you, Lennie

Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given expression.


Rewrite as


Factor to get


Photobucket - Video and Image HostingCancel out the common terms.

Simplify


So simplifies to .


In other words, where


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If we extablish an identity:
(cos^2 A)/(1 + sin A) would equal which of the following?
-----------------
cos^2 A = 1 - sin^2 A
-----------------
Your Problem:
cos^2 A / (1 + sin A)
= (1 - sin^2 A)/(1+sin A)
= [(1-sin A)(1+sin A)]/(1+sin A)
= 1 - sin A
-------------------------
Cheers,
Stan H.

1. cos^2 A + cot A cos A
2. 1 + sin A
3. 1 - sin A
4. 1