Question

Verifying Trig Functions

Answer 1

The answer to your question is below

Explanation:

csc α - cot α =
`(sin \alpha )/(1 + cos \alpha )`

Work with the left part

`(1)/(sin\alpha ) - (cos \alpha )/(sin \alpha)`

Simplify

`(1 - cos\alpha )/(sin\alpha )`

Multiply by the reciprocal

`(1 - cos\alpha )/(sin \alpha ) x (1 + cos\alpha )/(1 + cos\alpha )`

Simplify

`(1 - cos^(2)\alpha)/(sin\alpha (1 + cos\alpha))`

Remember that

sin²α = 1 -cos²α

Substitute the previous equation

`(sin^(2)\alpha )/(sin\alpha(1 + cos\alpha ) )`

Simplify

`(sin\alpha)/(1 + cos \alpha)`

The identity i proved.