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Question
Prove that (cosec A - sin A)( sec A - cos A) sec2 A = tan A.
Solution
LHS = (cosec A - sin A)(sec A - cos A). sec2A
= `(1/sin A - sin A).(1/cos A - cos A). 1/cos^2 A`
= `(1- sin^2A)/sin A.(1- cos^2 A)/(cos A) xx 1/cos^2 A`
= `cos^2 A/sin A xx sin^2 A/cos A xx 1/cos^2 A ....[ ∵ ( 1 - sin^2 A) = cos^2 A, 1 - cos^2 A = sin^2 A]`
= `sin A/cos A = tan A`
= RHS
Hence proved.
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