Prove that (cosec A - sin A) (sec A - cos A) sec^2 A= tan A..
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Answer:
L.H.S. = (cosec A – sin A)(sec A – cos A). sec2 A
= (1/sin A – sin A). (1/cos A – cos A). 1/cos2 A
= (1 – sin2 A/sin A) × (1 – cos2 A/cos A) × 1/cos2 a
= cos2 A/sin A × sin2 A/cos A × 1/cos2 A
[∵ (1 – sin2 A) = cos2 A]
[∵ 1 – cos2 A = sin2 A]
= sin A/cos A = tan A
= R.H.S.
Hence proved
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