Question

1+cosA/sinA=sinA/1-cosA

Answer 1

=1+cosA/sinA 
=sinA+cosA/sinA(sin^2A+cos^2=1)=(sin^2=1-cos^2) =sinA=1-cosA
=sinA+cosA/1-cosA
=sinA/1-cosA=1-cosA/cosA
=sinA/1-cosA(1)
=sinA/1-cosA\\

hence proved

Answer 2

1+cos A
 sin A
on multiply both numinator and denominator by sinA
(1+cosA)  × sinA
 sinA            sin A
(1+cosA) sin A      ⇒ (1+cosA)sinA            as use sin²A+cos²A=1
   Sin²A                      (1-cos²A)
(1+cosA) sinA              as use a²-b²=(a+b)(a-b)
(1+cosA)(1-cosA)
sinA         = RHS
(1-cosA)
Hence Proved