Question

Prove that : cos A / (1-tanA) + sinA /( 1-cotA) = sinA + cos A ​

Answer 1

Answer:

L.H.S. = cos A/1 – tanA + sin A/1 – cot A

= cos A/1 – sin A/cos A + sin A/1 – cos A/sin A

= cos A/(cos A – sin A)/cosA + sin A/(sin A – cos A)/sin A

= cos2 A/cos A – sinA + sin2 A/sinA – cos A

= cos2 A – sin2A/(cos A – sin A)

= (cos A + sin A)(cos A – sin A)/(cos A – sin A)

= cos A + sin A

= R.H.S.

Hence proved