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प्रश्न
Find the value of `tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
उत्तर
We know
`tan^-1x-tan^-1y=tan^-1 (x-y)/(1+xy),xy>1`
Now,
`tan^-1 (x/y)-tan^-1((x-y)/(x+y))`
`=tan^-1{(x/y-(x-y)/(x+y))/(1+x/y((x-y)/(x+y)))}`
`=tan^-1{((x^2+xy-xy+y^2)/(y(x+y)))/((x^2+y^2+xy-xy)/(y(x+y)))}`
`=tan^-1 1`
`=tan^-1(tan pi/4)`
`=pi/4`
`thereforetan^-1(x/y)-tan^-1((x-y)/(x+y))=pi/4`
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