Consider the following statements:
Assertion $(A)$: When $x, y, z$ are positive numbers, then $\operatorname{Tan}^{-1}\left(\sqrt{\frac{x(x+y+z)}{y z}}\right)+\operatorname{Tan}^{-1}\left(\sqrt{\frac{y(x+y+z)}{x z}}\right)+\operatorname{Tan}^{-1}\left(\sqrt{\frac{z(x+y+z)}{x y}}\right) = \pi$
Reason $(R)$: $\operatorname{Tan}^{-1} a + \operatorname{Tan}^{-1} b = \operatorname{Tan}^{-1}\left(\frac{a+b}{1-ab}\right)$ if $a > 0$ and $b > 0$ and $ab < 1$.

• A
  Both $(A)$ and $(R)$ are true, $(R)$ is the correct explanation of $(A)$
• B
  Both $(A)$ and $(R)$ are true, $(R)$ is not the correct explanation of $(A)$
• C
  $(A)$ is true, but $(R)$ is false
• D
  $(A)$ is false, but $(R)$ is true