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Evaluate: int(cosx)/(sin(x-pi/6)sin(x+pi...

Evaluate: `int(cosx)/(sin(x-pi/6)sin(x+pi/6))dx`

Text Solution

Verified by Experts

` I =int(cosx)/(sin(x-(pi)/(6))sin(x+(pi)/(6)))dx`
`=int(cosx)/(sin^(2)x-"sin"^(2)(pi)/(6))dx`
Let `sinx=t`
or `dt=cosx dx`
` :. I=int(dt)/(t^(2)-(1)/(4))`
`=(1)/(2(1)/(2))log|(t-(1)/(2))/(t+(1)/(2))|+C`
`=log|(2t-1)/(2t+1)|+C`
`=log|(2sinx-1)/(2sinx+1)|+C`
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