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JEE Mains · Maths · STD 11 - 3. trignometrical ratios,functions and identities
Let \(\tan \alpha, \tan \beta\) and \(\tan \gamma ; \alpha, \beta, \gamma \neq \frac{(2 n -1) \pi}{2}\) \(n \in N\) be the slopes of three line segments \(OA,OB\) and \(OC\), respectively, where \(O\) is origin.If circumcentre of \(\Delta ABC\) coincides with origin and its orthocentre lies on \(y-\)axis, then the value of \(\left(\frac{\cos 3 \alpha+\cos 3 \beta+\cos 3 \gamma}{\cos \alpha \cos \beta \cos \gamma}\right)^{2}\) is equal to :
- A \(144\)
- B \(169\)
- C \(121\)
- D \(100\)
Answer & Solution
Correct Answer
(A) \(144\)
Step-by-step Solution
Detailed explanation
Since orthocentre and circumcentre both lies on \(y\) -axis \(\Rightarrow\) Centroid also lies on \(y-\)axis \(\Rightarrow \Sigma \cos \alpha=0\) \(\quad \cos \alpha+\cos \beta+\cos \gamma=0\)…
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