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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).
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