Question

If $\text{cosec}A+\cot A=$ $\frac{11}{2}$, then $\tan A$ is equal to

• A. $\frac{21}{12}$
• B. $\frac{15}{16}$
• C. $\frac{44}{117}$
• D. $\frac{117}{43}$

Answer 1

Answer: (C)

$\frac{44}{117}$

Given, $\text{cosec}A+\cot A=\frac{11}{2}$ ....... (1)

Thus $\frac{1}{\text{cosec}A+\cot A}=\frac{2}{11}$

$\Rightarrow \text{cosec}A-\cot A=\frac{2}{11}$ .......... (2) $[\because cose{c}^{2}x-co{t}^{2}x=1]$

On subtracting $\left(1\right)-\left(2\right)$, we get

$2\cot A=\frac{11}{2}-\frac{2}{11}=\frac{117}{22}$

$\Rightarrow \cot A=\frac{117}{44}$

Therefore, $\tan A=\frac{44}{117}$