Question

30. Prove that cosA/1-tanA+sinA/1-cos A =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.

Answer 2

Answer:

LHS

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

=cos A/(1 - sin A/cos A) + sin A/(1 - cos A/sin A)

=cos²A/ (cos A - sin A) + sin²A / (sin A - cos A)

=cos²A/ (cos A - sin A) - sin²A / (cos A - sin A)

=(cos ² A - sin ² A) / (cos A - sin A)

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

=cos A + sin A i.e RHS

Step-by-step explanation: