Solve the Following Equation: Sin 2 X − Sin 4 X + Sin 6 X = 0

प्रश्न

Solve the following equation:

\[\sin 2x - \sin 4x + \sin 6x = 0\]

बेरीज

उत्तर

\[\sin 2x - \sin 4x + \sin 6x = 0\].
\[\Rightarrow 2 \sin \left( \frac{8x}{2} \right) \cos \left( \frac{4x}{2} \right) - \sin4x = 0\]
\[ \Rightarrow 2 \sin4x \cos2x - \sin4x = 0\]
\[ \Rightarrow \sin4x ( 2 \cos2x - 1) = 0\]

\[\Rightarrow \sin 4x = 0\] or

\[2 \cos2x - 1 = 0\]

\[\Rightarrow 4x = n\pi\],

\[n \in Z\] or

\[\cos2x = \frac{1}{2} \Rightarrow \cos2x = \cos \frac{\pi}{3}\]

\[\Rightarrow x = \frac{n\pi}{4}, n \in Z\] or

\[\Rightarrow x = \frac{n\pi}{4}, n \in Z\]

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Trigonometric Equations

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Q 4.9 Q 4.8 Q 5.1

पाठ 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २२]

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आर.डी. शर्मा Mathematics [English] Class 11

पाठ 11 Trigonometric equations
Exercise 11.1 | Q 4.9 | पृष्ठ २२

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Trigonometric Equations

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