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CBSE Class 12 Math 2013 Solved Paper

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Question : 1 of 29
Marks: +1, -0
Write the principal value of tan−1 (1) + cos−1(−12)
Solution:  
Let tan−1 (1) = y
⇒ tan y = 1 = tan (π4) ⇒ y = π4
⇒ tan−1(1) = π4
cos−1(−12) = z
⇒ cos z = −12 = - cos π3 = cos (π−π3) = cos (2π3)
⇒ z = 2π3 ⇒ cos−1(−12) = 2π3
∴ tan−1 (1) + cos−1(−12) = π4+2π3 = 11π12
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