Assertion : The value of $\tan \{\cos^{- 1} \frac{4}{5} + \tan^{- 1} \frac{2}{3}\}$ is $17 / 6$
Reason: $\tan^{- 1} x + \tan^{- 1} y = \tan^{- 1} (\frac{x - y}{1 + x y})$

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Assertion is incorrect, reason is correct.

Assertion is correct, reason is correct; reason is not a correct explanation for assertion

Assertion is correct, reason is correct; reason is a correct explanation for assertion.

Assertion is correct, reason is incorrect

answer is C.

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Detailed Solution

We have,

$\begin{array}{l} \tan (\cos^{- 1} \frac{4}{5} + \tan^{- 1} \frac{2}{3}) \\ = \tan (\tan^{- 1} (\frac{\sqrt{1 - \frac{16}{25}}}{\frac{4}{5}}) + \tan^{- 1} \frac{2}{3}) \\ = \tan (\tan^{- 1} \frac{3}{4} + \tan^{- 1} \frac{2}{3}) \\ = \tan (\tan^{- 1} \frac{\frac{3}{4} + \frac{2}{3}}{1 - \frac{3}{4} \cdot \frac{2}{3}}) \\ = \tan (\tan^{- 1} \frac{17}{6}) = \frac{17}{6} \end{array}$