(1+cosA)/sinA=11/2

2sin²(A/2)/2sin(A/2)cos(A/2)=cot(A/2)=11/2=>tanA/2=2/11

tanA=2tan(A/2)/1-tan²(A/2)

substituting the value of tanA/2

we get tanA=(44/105)

cosec A +  cot A

1 / sin A + cos A / sin A

(1+ cos A) / sin A

2 cos² A / 2  /  2 sin A/2 cos A/2

cot A/2 =  11/2

tan A/2 = 2/11

tan A = 2 tan A/2 / (1 - tan²A/2)

Here is an easy method:

Becoz plug in the value of to get and just subtract these to get the value of