Verified Solution • 2025–26 Session moderate

QJEEM22Ma562e: JEE Main 2022 Mathematics - Class 12 JEEM22Ma562e Solution: If the inverse trigonometric functions take principal values…

If the inverse trigonometric functions take principal values then

cos⁡−1(310cos⁡(tan⁡−1(43))+25sin⁡(tan⁡−1(43))){\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right) + {2 \over 5}\sin \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right)} \right) is equal to :

Multiple Choice Options

  • A 0
  • B π4{\pi \over 4}
  • C π3{\pi \over 3}
  • D π6{\pi \over 6}

Step-by-Step Verified Solution

cos⁡−1(310cos⁡(tan⁡−1(43))+25sin⁡(tan⁡−1(43))){\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right) + {2 \over 5}\sin \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right)} \right)

=cos⁡−1(310 . 35+25 . 45)= {\cos ^{ - 1}}\left( {{3 \over {10}}\,.\,{3 \over 5} + {2 \over 5}\,.\,{4 \over 5}} \right)

=cos⁡−1(12)=π3= {\cos ^{ - 1}}\left( {{1 \over 2}} \right) = {\pi \over 3}

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