If we consider only the principle values of the inverse trigonometric functions, then the value of $t a n (c o s^{- 1} \frac{1}{5 \sqrt{2}} - s i n^{- 1} \frac{4}{\sqrt{17}})$

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Solution

The correct option is D

$t a n (c o s^{- 1} \frac{1}{5 \sqrt{2}} - s i n^{- 1} \frac{4}{\sqrt{17}})$
$= t a n [t a n^{- 1} (\frac{7}{1}) - t a n^{- 1} (\frac{4}{1})]$
$= t a n (t a n^{- 1} - t a n^{- 1} 4) = t a n (t a n^{- 1} \frac{7 - 4}{1 + 7 \times 4})$
$= t a n (t a n^{- 1} \frac{3}{29}) = \frac{3}{29}$

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Similar questions

t a n (c o s^{- 1} \frac{1}{5 \sqrt{2}} - s i n^{- 1} \frac{4}{\sqrt{17}})

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