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AP EAMCET · Maths · Trigonometric Ratios & Identities

If the general solution set of \(\sin x+3 \sin 3 x+\sin 5 x=0\) is S , then \(\{\sin \alpha / \alpha \in S\}=\)

  1. A \(\{1,-1,0\}\)
  2. B \(\left\{\frac{1}{2}, \frac{-1}{2}, 0,1,-1\right\}\)
  3. C \(\left\{\frac{\sqrt{3}}{2}, 0, \frac{-\sqrt{3}}{2}\right\}\)
  4. D \(\left\{1,-1, \frac{\sqrt{3}}{2}, 0, \frac{-\sqrt{3}}{2}\right\}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\left\{\frac{\sqrt{3}}{2}, 0, \frac{-\sqrt{3}}{2}\right\}\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \text { } \sin x+\sin 5 x+3 \sin 3 x=0 \\ & \Rightarrow 2 \sin 3 x \cos 2 x+3 \sin 3 x=0 \\ & \Rightarrow \sin 3 x(2 \cos 2 x+3)=0 \\ & \Rightarrow \sin 3 x=0\left(\because \cos 2 x \neq \frac{-3}{2}\right) \\ & \Rightarrow 3 x=0, \pi, 2 \pi, 3 \pi, 4 \pi, 5…

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