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1. Prove thatsin2A tan A + cos2A.cot A +2 sin A. Cos A = tan A + cot A​

Answer»

ong>Answer:

LHS = RHS

= sin²A × tan A + cos² A × cot A + 2 × sin A × COS A

= sin³ A / cos A + cos³ A / sin A +2 sin A cos A

= ( sin⁴ A + cos⁴ A + 2 sin² A cos A ) / sin A cos A

= ( sin² A + cos² A )² / sin A cos A

= 1²/sin A cos A

= 1/ sin A cos A

= ( sin² A + co²A / sin A cos A )

= sin² A / sin A cos A + co² A / sin A cos A

= sin A / cos A + cos A / sin A

= tan A + cot A = RHS

LHS = RHS

sin²A × tan A + cos²A + cot A + 2 × sin A × cos A = tan A = cot A

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