Question

1+cosA/sinA + sinA/1+cosA = 2 cosecA

Answer 1

in the Left Hand Side
take the lcm first

(1+cosA)^2 +(sinA)^2/sinA (1+cosA)

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

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

2+2cosA/sinA (1+cosA)

2 (1+cosA)/sinA (1+cosA)

2/sinA

2cosecA
LHS=RHS
Proved!!!!
hope it helps