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Question
Prove the following identities:
cot2 A – cos2 A = cos2 A . cot2 A
Solution
L.H.S. = cot2 A – cos2 A
= `cos^2"A"/sin^2"A" - cos^2"A"`
= `(cos^2"A" - sin^2"A".cos^2"A")/(sin^2"A")`
= `(cos^2"A"(1 - sin^2"A"))/sin^2"A"`
= cot2 A (cos2 A)
= cos2 A . cot2 A
= R.H.S.
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