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प्रश्न
Evaluate the definite integral:
`int_(pi/6)^(pi/4) cosec x dx`
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उत्तर
`int_(pi/6)^(pi/4) cosec x dx`
`= [log ("cosec" x + cot x)]_(pi/6)^(pi/4)`
`= log ("cosec" pi/4 - "cot" pi/4) - log ("cosec" pi/6 - "cot" pi/6)`
`= log (sqrt2 - 1) - log (2 - sqrt3)`
`= log (sqrt2 - 1)/(2 - sqrt3)`
`because log m/n`
= log m = log n
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