1. ## Prove that

[1+cosA+sinA] = 1+sinA
[1+cosA-sinA] ... cosA

plzzzzz help meeee .......with this question....

2. Originally Posted by Sanjana Das
[1+cosA+sinA] = 1+sinA
[1+cosA-sinA] ... cosA

plzzzzz help meeee .......with this question....

$\displaystyle \frac{1+cosA+sinA}{1+cosA-sinA}$

=$\displaystyle \frac{2cos^2\frac{A}{2}+2cos\frac{A}{2}sin\frac{A} {2}}{2cos^2\frac{A}{2}-2cos\frac{A}{2}sin\frac{A}{2}}$

=$\displaystyle \frac{cos\frac{A}{2}+sin\frac{A}{2}}{cos\frac{A}{2 }-sin\frac{A}{2}}$

=$\displaystyle \frac{cos\frac{A}{2}+sin\frac{A}{2}}{cos\frac{A}{2 }-sin\frac{A}{2}}$.$\displaystyle \frac{cos\frac{A}{2}+sin\frac{A}{2}}{cos\frac{A}{2 }+sin\frac{A}{2}}$

=$\displaystyle \frac{1+sinA}{cosA}$

3. Originally Posted by Sanjana Das
[1+cosA+sinA] = 1+sinA
[1+cosA-sinA] ... cosA

plzzzzz help meeee .......with this question....
$\displaystyle \frac{1+cosA+sinA}{1+cosA-sinA}.\frac{cosA-sinA-1}{cosA-sinA-1}$

=$\displaystyle \frac{cos^2A-sin^2A-2sinA-1}{-2sinAcosA}$

=$\displaystyle \frac{1+sinA}{cosA}$