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The principal solution of the equation cot x=-√3  is - Mathematics and Statistics

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MCQ

The principal solution of the equation cot x=`-sqrt 3 ` is

Options

  • `pi/6`

  • `pi/3`

  • `(5pi)/6`

  • `(-5pi)/6`

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Solution

`(5pi)/6`

`cot x =-sqrt 3`
`cotx= -cotx`
we know `cotx` is negative in 2nd and 4th quadrant so, we convert this 2nd or 4th

now
`cotx=-cotx=cot (pi-(5pi)/6)`
`x=(5pi)/6`
also
`cotx=cot (2pi-(11pi)/6)`
`x=(11pi)/6`
only option given is `(5pi)/6`

Concept: Inverse Trigonometric Functions - Inverse Trigonometric Functions - Principal Value Branch
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