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Question

The value of cos1[sin(7π6)] is

A
5π3
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B
7π6
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C
π3
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D
7π6
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Solution

The correct option is C π3
cos1[sin(7π6)]=cos1[cos(π2+7π6)]=cos1[cos(10π6)]=cos1[cos(5π3)]=cos1[cos(2ππ3)]=cos1[cosπ3]=π3 (cos1(cosx)=x, x[0,π])


Alternate solution
cos1[sin(7π6)]
=cos1[sin(π+π6)]
=cos1[sin(π6)]
=cos1(12)
=π3, cos1(x)[0,π]

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