1.

सिद्ध कीजिए - `cot^(-1)((xy+1)/(x-y))+cot^(-1)((yz+1)/(y-z))+cot^(-1)((zx+1)/(z-x))=0,0 lt xy, yz, zx lt1.`

Answer» L.H.S.
`cot^(-1)((xy+1)/(x-y))+cot^(-1)((yz+1)/(y-z))+cot^(-1)((zx+1)/(z-x))`
`=tan^(-1)((x-y)/(1+xy))+tan^(-1)((y-z)/(1+yz))+tan^(-1)((z-x)/(1+zx))`
`" "[because cot^(-1)x=tan^(-1).(1)/(x)]`
`=(tan^(-1)x-tan^(-1)y)+(tan^(-1)y-tan^(-1)z)+(tan^(-1)z-tan^(-1)x),`
`[because 0 lt xy, yz, zx lt 1]" और "[ tan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(1+xy))" यदि " xy gt -1]`
= 0
= R.H.S.
यही सिद्ध करना था।


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