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CBSE Class 12 Math 2012 Solved Paper

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Question : 7 of 29
Marks: +1, -0
Write the principal value of cos⁡−1(12)\cos^{-1}\left(\frac{1}{2}\right) - 2 sin⁡−1(12)\sin^{-1}\left(\frac{1}{2}\right)
Solution:  
Principal value of cos⁡−1(12)\cos^{-1}\left(\frac{1}{2}\right) = π3\frac{\pi}{3}
Principal value of sin⁡−1(12)\sin^{-1}\left(\frac{1}{2}\right) = −π6-\frac{\pi}{6}
Hence principal value of cos⁡−1(12)\cos^{-1}\left(\frac{1}{2}\right) - 2 sin⁡−1(12)\sin^{-1}\left(\frac{1}{2}\right)
= π3−2(−π6)\frac{\pi}{3} - 2\left(-\frac{\pi}{6}\right)
= 2π3\frac{2\pi}{3}
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