Question

i hope someone can answer me as soon as possible​

Answer 1

LHS = $\frac{cos A}{1 - tan A} + \frac{sin A}{1 - cot A} = sin A + cos A$

= 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)

= (cos² A - sin² A) / (cos A - sin A)

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

=cos A + sin A = RHS