If tan^-1x+tan^-1y+tan^-1z=/2 and (x-y)²+(y-z)²+(z-x)²=0,then x²+y²+z² equals

a.0

b.4

c.1

d.none of these

Hi Meanka,

As each of the sqaure term in the sum≥0, the sum can be zero, only when x=y=z.

So 3tan^-1x= pie/2 (i assume you missed pie in the question). So x = tan(pie/6) = 1/root(3).

So the required sum = 1. Option (C).

Hope that helps.

Best Regards,

Ashwin (IIT Madras).