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JEE Main 20211 SeptemberEvening Shift
Exam
JEE Main
Year
2021
Date
1 September
Shift
Evening Shift
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main 2021 · 1 September · Evening Shift · Mathematics · Inverse Trigonometric Functions

^ - 1 ( ( - 5 ) ) + ^ - 1 ( ( 6 ) ) - ^ - 1 ( ( 12 ) ) is equal to...

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

Options

  1. A3π+13\pi + 1
  2. B3π−113\pi - 11
  3. C4π−114\pi - 11
  4. D4π−94\pi - 9

Correct answer

C. 4π−114\pi - 11

Step-by-step solution

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

=2π−5+(−2π+6)−(12−4π)= 2\pi - 5 + ( - 2\pi + 6 ) - ( 12 - 4\pi )

=4π−11= 4\pi - 11

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