The value of `cot(cose c^(-1)(5/3)+ tan^(-1)(2/3)) is: (1) `6/(17)` (2) `3/(17)` (2) `4/(17)` (4) `5/(17)`

Explanation

To solve the problem, we need to find the value of \( \cot\left(\csc^{-1}\left(\frac{5}{3}\right) + \tan^{-1}\left(\frac{2}{3}\right)\right) \).

### Step 1: Understanding the Inverse Functions
Let \( \theta = \csc^{-1}\left(\frac{5}{3}\right) \). This implies that \( \csc(\theta) = \frac{5}{3} \).

### Step 2: Finding Sine and Cosine
From the definition of cosecant:
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