Question
Wed August 29, 2012 By:

(1+1/tan^2 A)(1+1/cot^2 A)=1/(sin^2 A- sin^4 A)

Expert Reply
Wed August 29, 2012
LHS =
(1+1/tan^2 A)(1+1/cot^2 A)
= [(1+tan^2 A)/tan^2 A][(1+cot^2 A)/cot^2 A]
= [sec^2 A/tan^2 A][cosec^2 A/cot^2 A]
= 1/sin^2A cos^2A
= 1/sin^2A (1-sin^2A)
= 1/sin^2A -sin^4A
= RHS
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