Q31 / 90 · JEE Main 2021 (01 Sep Shift 2) · Mathematics

$\cos^{- 1} (\cos (- 5)) + \sin^{- 1} (\sin (6)) - \tan^{- 1} (\tan (12))$ is equal to :
(The inverse trigonometric functions take the principal values)

A
$3 π + 1$
B
$3 π - 11$
Correct answer
C
$4 π - 11$
D
$4 π - 9$

Solution

$\cos^{- 1} (\cos (- 5)) + \sin^{- 1} (\sin (6) - \tan^{- 1} (\tan (12))$

$= 2 π - 5 + (- 2 π + 6) - (12 - 4 π)$

$= 4 π - 11$

Hence, the correct answer is option: 'C'.

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