If `x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r))` is equal to `pi` (b) `pi/2` (c) 0 (d) none of these

Explanation

Correct option is B)

`tan^(−1)A+tan^(−1)B+tan^(−1)C=tan^(−1)((A+B+C−ABC)/(1−AB−BC−AC)​)​`



`tan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r))`



`=tan^(−1)​(((-xyz)/(r^3)+1/(rxyz)(x^2y^2+y^2z^2+z^2x^2))/(1-1/(r^2)(x^2+y^2+z^2)))`
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