Question

(cosec A- Sin A)(Sec A-CosA) sec2A=Tan A​

Answer 1

Answer:

L.H.S. = (cosec A – sin A)(sec A – cos A). sec2 A

= (1/sin A – sin A). (1/cos A – cos A). 1/cos2 A

= (1 – sin2 A/sin A) × (1 – cos2 A/cos A) × 1/cos2 a

= cos2 A/sin A × sin2 A/cos A × 1/cos2 A

[∵ (1 – sin2 A) = cos2 A]

[∵ 1 – cos2 A = sin2 A]

= sin A/cos A = tan A

= R.H.S.

Hence proved.