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Find the principal value of sec^(-1)(...

Find the principal value of `sec^(-1)((-2)/(sqrt(3)))`

Text Solution

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Let `sec^(-1)(-2/sqrt3)=y`
`rArr secy=(-2)/sqrt3`
`:'` The principal value of `sec^(-1)x" is "[0,pi]-{pi/2}` and in this interval `sec((5pi)/6)=(-2)/sqrt3`
`:. Sec^(-1)((-2)/sqrt3)=(5pi)/6`
`:.` The principal value of `sec^(-1)(-2/sqrt3)" is "(5pi)/6`.
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