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JEE Main
Exam
JEE Main
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

JEE Main · Mathematics · Inverse Trigonometric Functions

If ^ -1 a+ ^ -1 b+ ^ -1 c=π , then which of the following is true?

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

Options

  1. Aabc=1a b c=1
  2. Ba+b−c=abca+b-c=\frac{a b}{c}
  3. Ca+b+c=abca+b+c=a b c
  4. Da+b+c=1a+b+c=1

Correct answer

C. a+b+c=abca+b+c=a b c

Step-by-step solution

tan⁡−1a+tan⁡−1b+tan⁡−1c=π⇒tan⁡−1(a+b+c−abc1−ab−bc−ca)=π⇒a+b+c−abc1−ab−bc−ca=tan⁡π=0⇒a+b+c=abc\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\end{aligned}
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