Question

Cos A/1-tan A -sin2A/cos A-sin A – = Sin A+ Cos A

Answer 1

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Sol:

cos A / (1 - tan A) + sin A /(1 - cot A) = sin A + cos A

LHS = cos A / (1 - tan A) + sin A /(1 - cot A)

= cos A / (cos A - sin A) + sin A / (sin A - cos A)

= cos A / (cos A - sin A) - sin A / (cos A - sin A)

= (cos A - sin A) / (cos A - sin A)

= (cos A + sin A) (cos A - sin A) / (cos A - sin A)

= (cos A + sin A).

Hence proved.

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