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
- A \(\left\{-1,-\frac{\sqrt{3}}{2}, \frac{\sqrt{3}}{2}, 1\right\}\)
- B \(\left\{-1, \frac{1}{2}, 1\right\}\)
- C \(\left\{-\frac{\sqrt{3}}{2}, 0,1, \frac{\sqrt{3}}{2}\right\}\)
- D \(\left\{-1,-\frac{1}{2}, \frac{1}{2}, 1\right\}\)
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 \\ &…
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