CPM Homework Help : PC3 Problem 8-99

Verify the following trigonometric identities.

$\cot^2\left(x\right)\left(\sec^2\left(x\right)-1\right)=1$
Hint (a):
Substitute a Pythagorean Identity for $\sec^{2}\left(x\right) − 1$ .

$\sin^2\left(α\right)-\cos^2\left(α\right)=1-2\cos^2\left(α\right)$
Hint (b):
Substitute the Fundamental Pythagorean Identity into the left side of the equation for $\sin^{2}\left(α\right)$ .