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TS EAMCET · Maths · Trigonometric Equations

If the general solution of \(\sin x+3 \sin 3 x+\sin 5 x=0\) is \(x=y\) then the set of all values of \(\cos y\) is

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

Answer & Solution

Correct Answer

(D) \(\left\{-1,-\frac{1}{2}, \frac{1}{2}, 1\right\}\)

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 \quad \Rightarrow \sin 3 x=0 \\ & \Rightarrow \quad x=0, \pi \\ & \text { So, } \quad y=0, \pi \Rightarrow \cos 0=1 \\ &…