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Question
Find the principal value of the following:
`sec^(-1) (2/sqrt(3))`
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Solution
Let `sec^(-1) (2/sqrt(3))` = y
Then sec y = `2/sqrt3= sec y(pi/6)`
We know that the range of the principal value branch of sec−1 is `[0,pi] - {pi/2}`.
Then `sec (pi/6) = 2/sqrt3`
Therefore, the principal value of `sec^(-1) (2/sqrt3)` is `pi/6`.
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