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Trigonometric Functions — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsTrigonometric Functions2 Marks
MCQ
If $\sin 2 x+\sin 4 x=2 \sin 3 x$, then $x=$
  • ✓
    $\frac{ n \pi}{3}$
  • B
    $n \pi+\frac{\pi}{3}$
  • C
    $2 n \pi \pm \frac{\pi}{3}$
  • D
    None of these
✓

Answer

Correct option: A.
$\frac{ n \pi}{3}$
(A) $\sin 2 x+\sin 4 x=2 \sin 3 x$
$\begin{array}{l}\Rightarrow 2 \sin 3 x \cos x-2 \sin 3 x=0 \\ \Rightarrow \sin 3 x=0 \text { or } \cos x=1 \Rightarrow 3 x= n \pi \text { or } x=2 n \pi\end{array}$
$\Rightarrow x=\frac{ n \pi}{3}$ or $x=2 n \pi$

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