Question

Prove that (cosec A - sin A) (sec A - cos A) = 1 / tan A + cot A​

Answer 1

Step-by-step explanation:

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][sin2 A/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.