Question

If $cosec\theta +cot\theta =\frac{11}{2}$, then $tan\theta =$

• A. $\frac{21}{22}$
• B. $\frac{15}{16}$
• C. $\frac{44}{117}$
• D. $\frac{117}{44}$

Answer 1

The correct option is C

$\frac{44}{117}$

$\frac{44}{117}$

We have:

$cosec\theta +cot\theta =\frac{11}{2}....\left(1\right)$

$\Rightarrow \frac{1}{cosec\theta +cot\theta }=\frac{2}{11}$

$\Rightarrow \frac{cose{c}^2\theta -co{t}^2\theta }{cosec\theta +cot\theta }=\frac{2}{11}$

$\Rightarrow \frac{(cosec\theta +cot\theta )(cosec\theta -cot\theta )}{(cosec\theta +cot\theta )}=\frac{2}{11}$

$\therefore$ cosec A -cot $\theta =\frac{2}{11}.....\left(2\right)$

Subtracting (1)and (2):

$2cot\theta =\frac{11}{2}-\frac{2}{11}$

$\Rightarrow 2cot\theta =\frac{121-4}{22}$

$\Rightarrow 2cot\theta =\frac{117}{22}$

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

$\Rightarrow \frac{1}{tan\theta }=\frac{117}{44}$

$\Rightarrow tan\theta =\frac{44}{117}$