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

Question

Solve the following equation:

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

Sum

Solution

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

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

Chapter 11: Trigonometric equations - Exercise 11.1 [Page 22]

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RD Sharma Mathematics [English] Class 11

Chapter 11 Trigonometric equations
Exercise 11.1 | Q 4.9 | Page 22

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