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प्रश्न
Solve the following equation for x:
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
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उत्तर
`3sin^-1 (2x)/(1+x^2)-4cos^-1 (1-x^2)/(1+x^2)+2tan^-1 (2x)/(1-x^2)=pi/3`
`=>6tan^-1x-8tan^-1x+4tan^-1x=pi/3` `[because 2tan^-1x=sin^-1((2x)/(1+x^2)),2tan^-1x=cos^-1((1-x^2)/(1+x^2))and 2tan^-1x=tan^-1((2x)/(1-x^2))]`
`=>2tan^-1x=pi/3`
`=>tan^-1x=pi/6`
`=>x=tan pi/6`
`=>x=1/sqrt3`
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