Verified Solution • 2025–26 Session moderate

QJEEM24Mab820: JEE Main 2024 Mathematics - Class 12 JEEM24Mab820 Solution: If and , then is equal to

If a=sin⁡−1(sin⁡(5))a=\sin ^{-1}(\sin (5)) and b=cos⁡−1(cos⁡(5))b=\cos ^{-1}(\cos (5)) , then a2+b2a^2+b^2 is equal to

Multiple Choice Options

  • A 25
  • B 4π2+254 \pi^2+25
  • C 8π2−40π+508 \pi^2-40 \pi+50
  • D 4π2−20π+504 \pi^2-20 \pi+50

Step-by-Step Verified Solution

amp;a=sin⁡−1(sin⁡5)=5−2πamp; and b=cos⁡−1(cos⁡5)=2π−5amp;∴a2+b2=(5−2π)2+(2π−5)2amp;=8π2−40π+50\begin{aligned}& a=\sin ^{-1}(\sin 5)=5-2 \pi \\& \text { and } b=\cos ^{-1}(\cos 5)=2 \pi-5 \\& \therefore a^2+b^2=(5-2 \pi)^2+(2 \pi-5)^2 \\& =8 \pi^2-40 \pi+50\end{aligned}

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