Question

$cot\left(cosec^{-1} \frac{5}{3} + tan^{-1} \frac{2}{3}\right) =$

• A. $\frac{6}{17}$
• B. $\frac{3}{17}$
• C. $\frac{4}{17}$
• D. $\frac{5}{17}$

Answer 1

Answer: (A)

$\frac{6}{17}$

Answer 2

$cot\left(cosec^{-1} \frac{5}{3} + tan^{-1} \frac{2}{3}\right)$ $= cot\left(tan^{-1} \frac{3}{4} + tan^{-1} \frac{2}{3}\right)$ $=cot\left(tan^{-1} \left(\frac{\frac{3}{4} + \frac{2}{3}}{1-\frac{3}{4}\cdot\frac{2}{3}}\right)\right)$ $= cot \left(tan^{-1}\left(\frac{17}{6}\right)\right)$ $= cot\left(cot^{-1}\left(\frac{6}{17}\right)\right) = \frac{6}{17}$.