Question

1+cos a/sin a +sin a/1+cos a =2cosec a

Answer 1

Let us start with the LHS 

LHS = 1 + cosA/sinA  +  sinA / 1+ cosA

here , LCM = sinA(1+ cosA)

We know that ,

sin²A + cos²A = 1 

Hence,

1 + cosA gets cancelled , ( in numerator and denominator).

= 2 / sinA

= 2* 1/sinA

We know that , 1/sinA  = cosec A

Hence,

= 2*1/sinA = 2* cosecA = 2cosecA = RHS

PROVED.

Answer 2

this is the solution