Question

Verifying Trig Functions

Answer 1

Answer:

The answer to your question is below

Step-by-step explanation:

                csc α - cot α = $\frac{sin \alpha }{1 + cos \alpha }$

Work with the left part

                $\frac{1}{sin\alpha } - \frac{cos \alpha }{sin \alpha}$

Simplify

                $\frac{1 - cos\alpha }{sin\alpha }$

Multiply by the reciprocal

 $\frac{1 - cos\alpha }{sin \alpha } x \frac{1 + cos\alpha }{1 + cos\alpha }$                                  

Simplify

$\frac{1 - cos^{2}\alpha}{sin\alpha (1 + cos\alpha)}$

Remember that

                 sin²α = 1 -cos²α

Substitute the previous equation

$\frac{sin^{2}\alpha }{sin\alpha(1 + cos\alpha ) }$

Simplify

$\frac{sin\alpha}{1 + cos \alpha}$      

The identity i proved.