cosec A + cot A = 11/2 ... (1)
(cosec A + cot A) x (cosec A - cot A)/(cosec A - cot A) = 11/2
(cosec 2a - cot^2 A) /(cosec A - cot A ) = 11/2
Now cosec^2 A - cot^2 A = 1
Therefore, 1/(cosecA - cotA) = 11/2
cosec A - cot A = 2/11 ... (2)
From (1) and (2), we get,
- 2 cot A = 2/11 -11/2 = -117/22
cot A = 117/44
Therefore, tan A = 1/cot A = 44/117