Find the value of $$tan$$⁡$$cos$$−$$1$$⁡$$12+$$$$tan$$−$$1$$⁡−$$13$$

$$Lety=$$$$tan$$⁡$$cos$$−$$1$$⁡$$12+$$$$tan$$−$$1$$⁡−$$13=$$$$tan$$⁡π$$3+$$−π$$6=$$$$tan$$⁡π$$6=13$$

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Question

Find the value of $\tan [\cos^{- 1} (\frac{1}{2}) + \tan^{- 1} (- \frac{1}{\sqrt{3}})]$

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Solution

Let
$\begin{matrix} y = \tan [\cos^{- 1} (\frac{1}{2}) + \tan^{- 1} (- \frac{1}{\sqrt{3}})] \\ = \tan [\frac{π}{3} + (- \frac{π}{6})] = \tan (\frac{π}{6}) = \frac{1}{\sqrt{3}} \end{matrix}$

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