JEE Mains · Maths · STD 11 - Trigonometrical equations
If the lengths of the sides of a triangle are in \(A.P.\) and the greatest angle is double the smallest, then a ratio of lengths of the sides of this triangle
- A \(4 : 5 : 6\)
- B \(5 : 6 : 7\)
- C \(3 : 4 : 5\)
- D \(5 : 9 : 13\)
Answer & Solution
Correct Answer
(A) \(4 : 5 : 6\)
Step-by-step Solution
Detailed explanation
Given \(2b=a+c\) Let \(A=\theta \), \(B=\pi -3\theta \), \(C=2\theta \) \(2\sin\,B\,=\,\sin\,A\,+\,\sin\,C\) \(2\sin\,3\theta = \sin\theta +\sin2\theta \) \(2(3-4\sin^2\theta )\) \(=\) \((1+2\cos\theta )\) \(\Rightarrow 8\cos^2\theta \,-\,2\cos\theta \,-\,3\,=\,0\)…
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