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Sin2A and Cos2A in Terms of tanA

tan3 tan-1 3 ...

Question

$t a n (3 t a n^{- 1} 3) + c o s (3 c o s^{- 1} (1 / 3)) + 1$ is equal to

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9/13

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4/27

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295/351

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Solution

The correct option is B 295/351
Given, $tan (3 {tan}^{- 1} 3) + cos (3 {cos}^{- 1} (1 / 3)) + 1 = tan ({tan}^{- 1} (\frac{9 - 27}{1 - 27})) + cos ({cos}^{- 1} (\frac{4}{27} + 1)) + 1 = - tan ({tan}^{- 1} (\frac{9}{13})) + cos ({cos}^{- 1} (- \frac{23}{27})) + 1 = \frac{9}{13} - \frac{23}{27} + 1 = \frac{295}{351}$

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