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Solve the following equation: sin x + sin 5 x = sin 3 x

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प्रश्न

Solve the following equation:

\[\sin x + \sin 5x = \sin 3x\]
योग
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उत्तर

\[\sin x + \sin5x = \sin3x\]
\[\Rightarrow 2 \sin\left( \frac{6x}{2} \right) \cos \left( \frac{4x}{2} \right) = \sin3x\]
\[ \Rightarrow 2 \sin3x \cos2x = \sin3x\]
\[ \Rightarrow 2 \sin3x \cos2x - \sin3x = 0\]
\[ \Rightarrow \sin3x (2 \cos2x - 1) = 0\]
\[\Rightarrow \sin3x = 0\] or
\[(2 \cos2x - 1) = 0\]
\[\Rightarrow \sin3x = \sin 0\] or
\[\cos2x = \frac{1}{2} = \cos \frac{\pi}{3}\]
\[\cos2x = \frac{1}{2} = \cos \frac{\pi}{3}\] or
\[2x = 2m\pi \pm \frac{\pi}{3}\]
⇒ \[x = \frac{n\pi}{3}, n \in Z\] or
\[x = m\pi \pm \frac{\pi}{6}, m \in Z\]
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अध्याय 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २२]

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आर.डी. शर्मा Mathematics [English] Class 11
अध्याय 11 Trigonometric equations
Exercise 11.1 | Q 4.3 | पृष्ठ २२

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