The value of `tan[cos^(-1)(4/5)+tan^(-1)(2/3)]` is `6/(17)` (b) `7/(16)` (c) `(16)/7` (d) none of these

Explanation

To find the value of \( \tan\left(\cos^{-1}\left(\frac{4}{5}\right) + \tan^{-1}\left(\frac{2}{3}\right)\right) \), we can use the following steps:

### Step 1: Convert \( \cos^{-1}\left(\frac{4}{5}\right) \) to a tangent form
Let \( \theta = \cos^{-1}\left(\frac{4}{5}\right) \). Then, we know that:
\[ \cos(\theta) = \frac{4}{5} \]
To find \( \sin(\theta) \), we can use the Pythagorean identity:
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