### Home > PC3 > Chapter 10 > Lesson 10.2.3 > Problem10-146

10-146.

This problem is a checkpoint for simplifying trigonometric expressions and verifying trigonometric identities.

Simplify:

1. $(\csc(x) + \cot(x))(1 - \cos(x))$

1. $\frac { \operatorname { cos } ( x ) } { \operatorname { sec } ( x ) } + \frac { \operatorname { sin } ( x ) } { \operatorname { csc } ( x ) }$

1. Verify: $\frac { \sin ( x ) } { 1 + \cos ( x ) } + \frac { 1 + \cos ( x ) } { \sin ( x ) }= 2 \csc(x)$