A calculus of the absurd

7.3.4 Proving trigonometric identities
• Example 7.3.1 Prove that

$$\csc ^2(\theta )(\tan ^2(\theta ) - \sin ^2(\theta )) = \tan ^2(\theta )$$

This is a standard application of the general method of proving identities (as in Section 6.2); we pick one side (and my usual heuristic is to always start with the more complex side) and work toward the other side.