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Write the principal value of, cos^(-1)\ ...

Write the principal value of, `cos^(-1)\ (cos(7pi)/6)`

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Here, we will use `cos(pi+x) = cos(pi-x)`
`:. cos((7pi)/6) = cos(pi+pi/6) = cos(pi-pi/6)`
`= cos((5pi)/6)`
`:. cos^-1(cos((7pi)/6)) = cos^-1(cos((5pi)/6))`
`=(5pi)/6`, which is the required principal value as it is between `0` and `pi`.
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