Verified Solution • 2025–26 Session moderate

QJEEM21Ma73e7: JEE Main 2021 Mathematics - Class 12 JEEM21Ma73e7 Solution

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)

Multiple Choice Options

  • A 3 π\pi −- 11
  • B 4 π\pi −- 9
  • C 4 π\pi −- 11
  • D 3 π\pi + 1

Step-by-Step Verified Solution

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

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

=4π−11= 4\pi - 11 .

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