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  4. The value of tan(cos-1 (4/5) + tan-1 (2/3)) is

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Q. The value of $tan(cos^{-1} \frac{4}{5} + tan^{-1} \frac{2}{3})$ is

Inverse Trigonometric Functions

Solution:

$tan(cos^{-1} \frac{4}{5} + tan^{-1} \frac{2}{3})$
$= tan(tan^{-1}(\frac{3}{4}) + tan^{-1} \frac{2}{3}) $
$= \frac{\frac{3}{4} + \frac{2}{3}}{1 - \frac{3}{4} . \frac{2}{3}} = \frac{17}{6}$