Pythagorean identities Problems and Solutions

In trigonometry, the Pythagorean identities are used as formulas in trigonometry problems. Here is the list of the trigonometric questions with solutions for you to understand how to use the Pythagorean identities in trigonometric problems.

Evaluate $\dfrac{1+\cos{\theta}-\sin^2{\theta}}{\sin{\theta}(1+\cos{\theta})}$

Evaluate $\dfrac{1}{\sin{x}+1}$ $-$ $\dfrac{1}{\sin{x}-1}$

Evaluate $(\sec{x}+\tan{x})\bigg(\dfrac{1-\sin{x}}{\cos{x}}\bigg)$