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CBSE Class 12 Math 2022 Term I Solved Paper

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Question : 7 of 50
Marks: +1, -0
The principal value of cos⁡−1(12)+sin⁡−1(−12)\cos^{-1} \left( \frac{1}{2} \right) + \sin^{-1} \left( -\frac{1}{\sqrt{2}} \right) is
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Explanation: cos⁡−1(12)+sin⁡−1(−12)\cos^{-1} \left( \frac{1}{2} \right) + \sin^{-1} \left( \frac{-1}{\sqrt{2}} \right)
=cos⁡−1(cos⁡π3)−sin⁡−1(12)= \cos^{-1} \left( \cos \frac{\pi}{3} \right) - \sin^{-1} \left( \frac{1}{\sqrt{2}} \right)
=π3−sin⁡−1(sin⁡π4)= \frac{\pi}{3} - \sin^{-1} \left( \sin \frac{\pi}{4} \right)
=π3−π4=π12= \frac{\pi}{3} - \frac{\pi}{4} = \frac{\pi}{12}
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