A) \[\frac{1}{6}\]
B) \[\frac{3}{28}\]
C) \[\frac{1}{18}\]
D) \[\frac{44}{117}\]
Correct Answer: D
Solution :
[d] \[\because cosec\,\theta +cot\theta =\frac{11}{2}\] .........(1) \[\because cose{{c}^{2}}\theta -co{{t}^{2}}\theta =1\] \[(cosec\theta +cot\theta ).(cosec\theta -cot\theta )=1\] \[cosec\theta -cot\theta =\frac{1}{\cos ec\theta +\cot \theta }\] \[=\frac{2}{11}\] .........(2) \[\theta \]subtracting (1) from (2), we have \[2.cot\theta =\frac{11}{2}-\frac{2}{11}\] \[=2.cot\theta =\frac{121-4}{22}\] \[cot\theta =\frac{117}{44}\] \[=tan\theta =\frac{44}{117}\]. Hence, option [d] is correct.
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