If `cot^(-1)x+cot^(-1)y+cot^(-1)z=pi/2,x , y , z >0a n dx y<1,` then `x+y+z` is also equal to (a)`1/x+1/y+1/z` (b) `x y z` (c) `xy+yz+zx` (d) none of these

Explanation

`cot^-1x+cot^-1y+cot^-1z = pi/2`

`=>pi/2 - tan^-1x+pi/2 - tan^-1y+pi/2 - tan^-1z = pi/2`

`=>tan^-1x+tan^-1 y = pi - tan^-1z`

`=> tan^-1((x+y)/(1-xy)) = pi - tan^-1z`

`=>tan(tan^-1((x+y)/(1-xy))) = tan(pi - tan^-1z)`

`=>tan(tan^-1((x+y)/(1-xy))) =- tan(tan^-1z)`

`=>(x+y)/(1-xy) = -z`

`=>x+y = -z+xyz`

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