Find all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π.

Asked by maham237 @ in Mathematics viewed by 360 People

Find all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π. (enter your answers as a comma-separated list.)

Answered by maham237 @


Answer:

Solution: x=0,\dfrac{\pi}{3},\pi,\dfrac{5\pi}{3},2\pi

Step-by-step explanation:

Given: \sin 2x=\sin x

Using trigonometry formula:

\sin 2x=\sin x

2\sin x\cos x=\sin x

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

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

\sin x=0\text{ and }2\cos x-1=0

\sin x=0

x=0,\pi,2\pi

2\cos x=1

\cos x=\dfrac{1}{2}

x=\dfrac{\pi}{3},\dfrac{5\pi}{3}

Hence, The solutions of the given equation are x=0,\dfrac{\pi}{3},\pi,\dfrac{5\pi}{3},2\pi


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