Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

$$\begin{array}{rl}& \text{ Let }E=\cot \left({\mathrm{cosec}}^{-1}\frac{5}{3}+{\tan }^{-1}\frac{2}{3}\right)\\ & \Rightarrow E=\cot \left({\tan }^{-1}\left(\frac{3}{4}\right)+{\tan }^{-1}\left(\frac{2}{3}\right)\right)\\ & \Rightarrow E=\cot \left({\tan }^{-1}\left(\frac{\frac{3}{4}+\frac{2}{3}}{1-\frac{3}{4}\cdot \frac{2}{3}}\right)\right)\\ & \Rightarrow E=\cot \left({\tan }^{-1}\frac{17}{6}\right)=\frac{6}{17}.\end{array}$$