Question

prove that cosA/1-tanA +sinA/1-cotA =cosA+sinA​

Answer 1

Step-by-step explanation:

1. cosA/1-sinA/cosA +sinA/1-cosA/sinA
2. cosA/cosA-sinA/cosA+sinA/sinA-cosA/sinA
3. cos^2A/cosA-sinA+sin^2A/sinA-cosA
4. cos^2A/cosA-sinA - sinA/cosA-sinA
5. cos^2A-sin^2A/cosA-sinA
6. (cosA+sinA)(cosA-sinA)/(cosA-sinA)
7. cosA+sinA

Answer 2

Answer:

cosA+sinA

Step-by-step explanation:

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