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If x gt y gt z gt 0, then find the value...

If `x gt y gt z gt 0`, then find the value of `"cot"^(-1) (xy + 1)/(x - y) + cot^(-1).(yz + 1)/(y - z) + cot^(-1).(zx + 1)/(z - x)`

A

xyz

B

x+y+z

C

0

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
`cot^(-1)((xy+1)/(x-y))+cot^(-1)((yz+1)/(y-z))+cot^(-1)((zx+1)/(z-x))`
`rArrtan^(-1)((x-y)/(xy+1))+tan^(-1)((y-z)/(yz+1))+tan^(-1)((z-x)/(zx+1))`
`rArr(tan^(-1)x-tan^(-1)y)+(tan^(-1)y-tan^(-1)z)+(tan^(-1)z-tan^(-1)x)`
`=0[becausetan^(-1)x-tan^(-1)y=tan^(-1)((x-y)/(1+xy))]`
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