MHT CET · Maths · Inverse Trigonometric Functions
If \(\tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c=\pi\), then which of the following statement is true?
- A \(a+b-c=a b c\)
- B \(a+b+c=2 a b c\)
- C \(a b c=1\)
- D \(a+b+c=a b c\)
Answer & Solution
Correct Answer
(D) \(a+b+c=a b c\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \tan ^{-1} a+\tan ^{-1} b+\tan ^{-1} c=\pi \\ & \Rightarrow \tan ^{-1}\left(\frac{a+b+c-a b c}{1-a b-b c-c a}\right)=\pi \\ & \Rightarrow \frac{a+b+c-a b c}{1-a b-b c-c a}=\tan \pi=0 \\ & \Rightarrow a+b+c-a b c=0 \\ & \Rightarrow a+b+c=a b c\end{aligned}\)
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