Question

cos
A÷
1-tan A
+
sin A÷
1-cot A
= sin A +cos A​

Answer 1

I presume the problem is

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

Note the parantheses and the RHS.

LHS = cos A/{(cos A -sin A)/cos A}

+ sin A/{(sinA-cos A)/sin A}

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

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

= cos A + sin A = RHS ( modified)

Answer 2

Answer:

LHS = COSA / (1-TAN A) + SIN A / ( 1- COT )

COS A / (1-SINA / COSA ) + SINA / ( 1- COSA / SINA )

COS^2A/ ( COS A - SINA ) + SIN^2A / ( SINA- COS A)

COS^2A / COS A - SINA - SIN^2 A / COS A - SINA

COS^2 A - SIN^2 A / ( COS A- SINA )

( COSA - SINA) ( COSA + SINA) / ( COSA - SINA)

( COSA + SINA ) = RHS

HENCE; LHS = RHS