AP EAMCET · Maths · Trigonometric Equations
If \(\cos \alpha+3 \cos 3 \beta+5 \cos 5 \gamma=0\), \(\sin \alpha+3 \sin 3 \beta+5 \sin 5 \gamma=0\) and \(\cos 3 \alpha+27 \cos 9 \beta+125 \cos 15 \gamma=\left(\lambda^2-4\right)\) \(\cos (\alpha+3 \beta+5 \gamma)\), then \(\lambda\) is equal to
- A \(\pm 2 \sqrt{2}\)
- B \(\pm 2 \sqrt{5}\)
- C \(\pm \sqrt{7}\)
- D \(\pm \sqrt{29}\)
Answer & Solution
Correct Answer
(C) \(\pm \sqrt{7}\)
Step-by-step Solution
Detailed explanation
Given, \(\cos \alpha+3 \cos 3 \beta+5 \cos 5 \gamma=0\) ...(i) \(\sin \alpha+3 \sin 3 \beta+5 \sin 5 \gamma=0\) ...(ii) \(\cos 3 \alpha+27 \cos 9 \beta+125 \cos 15 \gamma\) \(=\left(\lambda^2-4\right) \cos (\alpha+3 \beta+5 \gamma)\) ...(iii) To find, \(\lambda=\) ? Let…
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