Question

Prove that: cosA / 1 - tanA + sinA / 1-cotA = cosA + sinA

Answer 1

the above one has sign mistake just instead of cos²A+sin²A, put cos²A-sin²A.

that's it.

Answer 2

Answer:

Step-by-step explanation:

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  That is  RHS