cotA-TanA=2cos^2A-1/sinA.cosA.
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LHS = cot A - tan A
= (cos A / sin A) - (sin A / cos A)
= (cos2A - sin2A) / (sin A cos A)
= [ cos2A - (1 - cos2A)] / (sin A cos A) {Since sin2Θ = 1 - cos2Θ }
= (cos2A - 1 + cos2A) / (sin A cos A)
= (2 cos2A - 1) / (sin A cos A)
= RHS
= (cos A / sin A) - (sin A / cos A)
= (cos2A - sin2A) / (sin A cos A)
= [ cos2A - (1 - cos2A)] / (sin A cos A) {Since sin2Θ = 1 - cos2Θ }
= (cos2A - 1 + cos2A) / (sin A cos A)
= (2 cos2A - 1) / (sin A cos A)
= RHS
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