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

Question

Solve the following equation:

\sin x + \sin 5 x = \sin 3 x

Sum

Solution

\sin x + \sin 5 x = \sin 3 x

\Rightarrow 2 \sin (\frac{6 x}{2}) \cos (\frac{4 x}{2}) = \sin 3 x

\Rightarrow 2 \sin 3 x \cos 2 x = \sin 3 x

\Rightarrow 2 \sin 3 x \cos 2 x - \sin 3 x = 0

\Rightarrow \sin 3 x (2 \cos 2 x - 1) = 0

\Rightarrow \sin 3 x = 0

(2 \cos 2 x - 1) = 0

\Rightarrow \sin 3 x = \sin 0

\cos 2 x = \frac{1}{2} = \cos \frac{π}{3}

\cos 2 x = \frac{1}{2} = \cos \frac{π}{3}

2 x = 2 m π \pm \frac{π}{3}

⇒

x = \frac{n π}{3}, n \in Z

x = m π \pm \frac{π}{6}, m \in Z

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Trigonometric Equations

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Q 4.3 Q 4.2 Q 4.4

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 4.3 | Page 22

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