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प्रश्न
Find the principal values of the following:
`cos^-1(sin (4pi)/3)`
उत्तर
Let `cos^-1(sin (4pi)/3) = y`
Then,
`cosy = sin (4pi)/3`
We know that the range of the principal value branch is [0, π].
Thus,
`cosy=sin (4pi)/3=-sqrt3/2=cos (5pi)/6`
`=>y=(5pi)/6in[0,pi]`
Hence, the principal value of `cos^-1(sin (4pi)/3)` is `(5pi)/6`.
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