Question

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

• A. $\frac{21}{22}$
• B. $\frac{15}{16}$
• C. $\frac{44}{117}$
• D. $\frac{117}{43}$

Answer 1

Answer: (C)

$\text{cosec}^2 A-\cot ^2 A=1 $....(i)
$\text{cosec} A+\cot A=\frac{11}{2}$....(ii)
dividing, we get $\text{cosec} A-\cot A=\frac{2}{11}$
subtracting (ii) from (i), $2 \cot A=\frac{117}{22} $
$\Rightarrow \tan A=\frac{44}{117}$