Maharashtra State BoardHSC Arts 12th Board Exam
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Evaluate : ∫1/(3+2sinx+cosx)dx - Mathematics and Statistics

Evaluate : `∫1/(3+2sinx+cosx)dx`

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Solution

let I=`∫1/(3+2sinx+cosx)dx`

put `tan(x/2)=t`

`x=2tan^-1t`

`dx=(2dt)/(1+t^2)` and `sinx=2t/(1+t^2), cosx((1-t^2)/(1+t^2))`

`therefore I=tan^-1[tan(x/2)+1]+c`

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