Answer:
see explanation
Step-by-step explanation:
Using the identities
1 - cos²x = sin²x
cotx = [tex]\frac{cosx}{sinx}[/tex] , cosecx = [tex]\frac{1}{sinx}[/tex]
Consider the left side
[tex]\frac{1}{1-cos\alpha }[/tex] - [tex]\frac{1}{1+cos\alpha }[/tex]
= [tex]\frac{1+cos\alpha - (1-cos\alpha )}{(1-cos\alpha )(1+cos\alpha )}[/tex]
= [tex]\frac{1+cos\alpha -1+cos\alpha }{1-cos^2\alpha }[/tex]
= [tex]\frac{2cos\alpha }{sin^2\alpha }[/tex]
= [tex]\frac{2cos\alpha }{sin\alpha }[/tex] × [tex]\frac{1}{sin\alpha }[/tex]
= 2cotα . cosecα
= right side , thus verified
