Step-by-step explanation:
[tex][csc \: x + cot \: x] [1 - cos \: x] \\ \\ = \bigg [\frac{1}{sin \: x} + \frac{cos \: x}{sin \: x} \bigg] [1 - cos \: x] \\ \\ = \bigg [\frac{1 + cos \: x}{sin \: x} \bigg] [1 - cos \: x] \\ \\ = \bigg [\frac{1 - cos ^{2} \: x}{sin \: x} \bigg] \\ \\ = \bigg [\frac{sin ^{2} \: x}{sin \: x} \bigg] \\ \\ \red{ \boxed { \bold{\therefore [csc \: x + cot \: x] [1 - cos \: x] = sin \: x }}}\\ [/tex]
