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प्रश्न
Find the principal value of the following:
`tan^-1(-1/sqrt3)`
उत्तर
We have `tan^-1(-1/sqrt3)=-tan^-1(1/sqrt3)` `[because tan^-1(-x)=-tan^-1x]`
Let `tan^-1(1/sqrt3)=y`
Then,
`tany=1/sqrt3`
We know that the range of the principal value branch is `(-pi/2,pi/2)`
Thus,
`tany=1/sqrt3=tan(pi/6)`
`=>y = pi/6`
`therefore tan^-1(-1/sqrt3)=-tan^-1(1/sqrt3)`
= - y
`=-pi/6in(-pi/2,pi/2)`
Hence, the principal value of `tan^-1(-1/sqrt3) is -pi/6.`
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