${sin}^{- 1} (sin 3) + {cos}^{- 1} (cos 3) + {tan}^{- 1} (tan 3) =$ _________.

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Solution

By checking the domain and solving, we get

$s i n^{- 1} (s i n 3) = π - 3$

=> $c o s^{- 1} (c o s 3) = 3$

=> $t a n^{- 1} (t a n 3) = 3 - π$

=> $s i n^{- 1} (s i n 3) + c o s^{- 1} (c o s 3) + t a n^{- 1} (t a n 3) = (π - 3) + (3) + (3 - π)$

=> $3$

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