Answer:
The answer to your question is below
Step-by-step explanation:
csc α - cot α = [tex]\frac{sin \alpha }{1 + cos \alpha }[/tex]
Work with the left part
[tex]\frac{1}{sin\alpha } - \frac{cos \alpha }{sin \alpha}[/tex]
Simplify
[tex]\frac{1 - cos\alpha }{sin\alpha }[/tex]
Multiply by the reciprocal
[tex]\frac{1 - cos\alpha }{sin \alpha } x \frac{1 + cos\alpha }{1 + cos\alpha }[/tex]
Simplify
[tex]\frac{1 - cos^{2}\alpha}{sin\alpha (1 + cos\alpha)}[/tex]
Remember that
sin²α = 1 -cos²α
Substitute the previous equation
[tex]\frac{sin^{2}\alpha }{sin\alpha(1 + cos\alpha ) }[/tex]
Simplify
[tex]\frac{sin\alpha}{1 + cos \alpha}[/tex]
The identity i proved.
