Question

cosA/(1-tanA)+sinA/(1-cotA)=sinA + cosA​

Answer 1

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.