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प्रश्न
Find the principal value of the following:
`tan^-1(2cos (2pi)/3)`
उत्तर
Let `tan^-1(2cos (2pi)/3)=y`
Then,
`tany=2cos (2pi)/3`
We know that the range of the principal value branch is `(-pi/2,pi/2)`
Thus,
`tany=2cos (2pi)/3 =2xx(-1)/2=-1=tan(-pi/4)`
`=>y=-pi/4in(-pi/2,pi/2)`
Hence, the principal value of `tan^-1(2cos (2pi)/3) is -pi/4.`
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