WBJEE · Maths · Inverse Trigonometric Functions
If \(\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi\), then \(\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)\) is equal to
- A \(0\)
- B \(1\)
- C \(6\)
- D \(12\)
Answer & Solution
Correct Answer
(C) \(6\)
Step-by-step Solution
Detailed explanation
Given: \(\cos ^{-1} \alpha+\cos ^{-1} \beta+\cos ^{-1} \gamma=3 \pi\) We know that: \(\cos ^{-1} x \in[0, \pi] \Rightarrow\) Max sum of three is \(3 \pi \Rightarrow \cos ^{-1} \alpha=\cos ^{-1} \beta=\cos ^{-1} \gamma=\pi \Rightarrow \alpha=\cos (\pi)=-1\) So:…
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