First slide

Properties of ITF

Question

The value of $\cot ({cosec}^{- 1} \frac{5}{3} + \tan^{- 1} \frac{2}{3})$ is

Moderate

A

6/17
B

3/17
C

4/17
D

5/17

Solution

$\begin{array}{l} Let E = \cot ({cosec}^{- 1} \frac{5}{3} + \tan^{- 1} \frac{2}{3}) \\ \Rightarrow E = \cot (\tan^{- 1} (\frac{3}{4}) + \tan^{- 1} (\frac{2}{3})) \\ \Rightarrow E = \cot (\tan^{- 1} (\frac{\frac{3}{4} + \frac{2}{3}}{1 - \frac{3}{4} \cdot \frac{2}{3}})) \\ \Rightarrow E = \cot (\tan^{- 1} \frac{17}{6}) = \frac{6}{17} \end{array}$

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