Question

__________
20. Prove that: /cosec A+1 1+SinA
/------------------- = -----------
V cosecA-1 cosA​

Answer 1

Answer:

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Step-by-step explanation:

Sol: LHS = (Cosec A - Sin A) (Sec A - Cos A) = (1/sin A - Sin A)(1/cos A - cos A) = [(1 - sin2 A)/sin A] [(1 - cos2 A)/cos A] = [(cos2 A)/sin A][sin2A/cos A] = sin A cos A RHS = 1 / (Tan A + Cot A)         = 1 / (sin A/cos A  + cos A/sin A)        = 1 / [(sin2 A + cos2 A)/sin A cos A]        = 1 / [1/sin A cos A]         = sin A cos A LHS = RHS Hence proved.