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Evaluate the Following: `Cosec^-1(-2/Sqrt3)+2cot^-1(-1)`

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Question

Evaluate the following:

`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`

Sum
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Solution

`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)=\text(cosec)^-1[\text(cosec)-pi/3)]+2cot^-1[cot((3pi)/4)]`

`=-pi/3+2xx(3pi)/4`

`=-pi/3+(3pi)/2`

`=(7pi)/6`

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