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Question
Prove that (cosec A – sin A)(sec A – cos A) sec2 A = tan A.
Solution
L.H.S = `(cosec A - sin A)(secA - cosA)sec^2A`
`= (1/sinA - sinA)(1/cosA - cosA)(1/cos^2A)`
`= ((1 - sin^2A)/sin A)((1- cos^2A)/cos A)(1/(cos^2A))`
`= cos^2A/sinA . sin^2A/cos A . 1/cos^2A`
`= sinA/cosA`
= tan A
= R.H.S
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