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Question

The value of cos1x+cos1(x2+1233x2) where (12x1) is equal to


A
π6
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B
π3
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C
π
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D
0
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Solution

The correct option is B π3
Let cos1x=y. Then x=cos y, such that 12x1,or0yπ3, and
x2+1233x2=12cos y+32sin y
=cosπ3cos y+sinπ3sin y=cos(π3y)
cos1(x2+1233x2)=π3y
because cos1(cos x)=x if 0xπ. Therefore, the given expression is equal to y+π3y=π3

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