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The principal values of `cos^(-1)(-sin(7pi)/(6))` is

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The principal values of `cos^(-1)(-sin(7pi)/(6))` is
A. `(5pi)/(3)`
B. `(7pi)/(6)`
C. `(pi)/(3)`
D. none of these
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We have
`cos^(-1)-sin(7pi)/(6)=cos^(-1)-sin(pi+(pi)/(6))=cos^(-1)sin(pi)/(6)`
`=(pi)/(2)-sin^(-1)sin(pi)/(6)=(pi)/(2)-(pi)/(6)=(pi)/(3)`
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