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Solve the Following Equation: Sin X + Sin 2 X + Sin 3 = 0

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प्रश्न

Solve the following equation:

\[\sin x + \sin 2x + \sin 3 = 0\]
योग
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उत्तर

\[\sin x + \sin 2x + \sin 3 = 0\]
\[\Rightarrow \sin x + \sin3x + \sin2x = 0\]
\[ \Rightarrow 2 \sin \left( \frac{4x}{2} \right) \cos \left( \frac{2x}{2} \right) + \sin2x = 0\]
\[ \Rightarrow 2 \sin2x\cos x + \sin2x = 0\]
\[ \Rightarrow \sin2x (2 \cos x + 1) = 0\]

\[\Rightarrow \sin2x = 0\] or
\[2 \cos x + 1 = 0\]
\[\Rightarrow \sin2x = \sin 0\] or
\[\cos x = - \frac{1}{2} \Rightarrow \cos x = \cos \frac{2\pi}{3}\]
⇒ \[x = \frac{n\pi}{2}, n \in Z\] or
\[x = 2m\pi \pm \frac{2\pi}{3}\],
\[m \in Z\]
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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 4.6 | पृष्ठ २२

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