Answer:
see explanation
Step-by-step explanation:
Using the identities
1 + cot²x = cosec²x
cosec²x = [tex]\frac{1}{sin^2x}[/tex] , cotx = [tex]\frac{cosx}{sinx}[/tex]
Consider the left side
cos²A + cos²A cot²A ← factor out cos²A from each term
= cos²A(1 + cot²A)
= cos²A × cosec²A
= cos²A × [tex]\frac{1}{sin^2A}[/tex]
= [tex]\frac{cos^2A}{sin^2A}[/tex]
= cot²A
= right side , thus proven
