Question

prove that cos A / 1-tan A plus sin A / 1- cot A is equal to sin A plus cos A​

Answer 1

Answer:given below

Step-by-step explanation:

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

LHS = cos A / (1 - tan A) + sin A /(1 - cot A)

      = cos2 A / (cos A - sin A) + sin2 A / (sin A - cos A)

      = cos2 A / (cos A - sin A) - sin2 A / (cos A - sin A)

      = (cos2 A - sin2 A) / (cos A - sin A)

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

      = (cos A + sin A).

Hence proved.