Prove Identities

Quote:

Originally Posted by satishgaire

hi,
can u help me?
I have spent over 2 hours trying to figure it out but was unsucessful. can you please prove the identities. thanks!
1) Cos X/Sec X - 1 - Cos X/tan^2 X = Cot^2 X

2) Sin X / 1 - Cos X + 1 - Cos X / Sin X = 2CSC X

hi

(1) Combine the fractions first to get .

$\frac{\sin^2 x+(1-\cos x)^2}{\sin x(1-\cos x)}$

$\frac{\sin^2 x+\cos^2 x+1-2\cos x}{\sin x(1-\cos x)}$

try continuing here .

(2) $\frac{\cos x}{\sec x-1}\cdot \frac{\sec x+1}{\sec x+1}-\frac{\cos x}{\tan^2 x}$

$\frac{\cos x\sec x+\cos x}{\sec^2 x-1 }-\frac{\cos x}{\tan^2 x}$

$\frac{1+\cos x}{\tan^2 x}-\frac{\cos x}{\tan^2 x}$

Then simplify .