Question

(cos×cosec-sin×sec)/cos+sin=cosec-sec

Answer 1

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.

brainliest me bro