If $ an ^{-1} a+ an ^{-1} b+ an ^{-1} c=\pi$, then which of the following is true?

Question

If $	an ^{-1} a+	an ^{-1} b+	an ^{-1} c=\pi$, then which of the following is true?

Aicharya · Accepted Answer

$\begin{aligned} & 	an ^{-1} a+	an ^{-1} b+	an ^{-1} c=\pi \ & \Rightarrow 	an ^{-1}\left(\frac{a+b+c-a b c}{1-a b-b c-c a}ight)=\pi \ & \Rightarrow \frac{a+b+c-a b c}{1-a b-b c-c a}=	an \pi=0 \ & \Rightarrow a+b+c=a b c\end{aligned}$

If $\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c=\pi$, then which of the following is true?

Solution