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Question: If \(\text{cosec }A + \cot A = \frac{11}{2},\) then \(\tan A =\)...

If cosec A+cot⁡A=112,\text{cosec }A + \cot A = \frac{11}{2}, then tan⁡A=\tan A =

A

2122\frac{21}{22}

B

1516\frac{15}{16}

C

44117\frac{44}{117}

D

11743\frac{117}{43}

Answer

44117\frac{44}{117}

Explanation

Solution

cosecA+cot⁡A=112⇒cosecA−cot⁡A=211\text{cosec}A + \cot A = \frac{11}{2} \Rightarrow \text{cosec}A - \cot A = \frac{2}{11}

Therefore 2cot⁡A=11722⇒tan⁡A=441172\cot A = \frac{117}{22} \Rightarrow \tan A = \frac{44}{117}.