Simplifying tan ^ 1( √(3)) ^ 1( 2) . tan ^ 1( √(3)) ^ 1( 2) = tan ^ 1( tan( π3)) ^ 1( π3) = tan ^ 1( tan( π3) ...

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Standard Formulae - 2

Simplify ta...

Question

Simplify ${tan}^{- 1} (\sqrt{3}) - {sec}^{- 1} (- 2)$

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Solution

Simplifying ${tan}^{- 1} (\sqrt{3}) - {sec}^{- 1} (- 2)$ .

${tan}^{- 1} (\sqrt{3}) - {sec}^{- 1} (- 2)$

$= {tan}^{- 1} (tan (\frac{π}{3})) - {sec}^{- 1} (- sec \frac{π}{3})$

$= {tan}^{- 1} (tan (\frac{π}{3})) - {sec}^{- 1} (sec (π - \frac{π}{3}))$

$= \frac{π}{3} - \frac{2 π}{3}$

$= - \frac{π}{3}$

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