How do you solve the equation \sin 2x-\sin x=0 on

aramutselv

aramutselv

Answered question

2021-12-08

How do you solve the equation sin2xsinx=0 on the interval [0,2π]?

Answer & Explanation

raefx88y

raefx88y

Beginner2021-12-09Added 26 answers

Given:
sin2xsinx=0
Let us use the trigonometric identity sin2x=2sinxcosx:
2sinxcosxsinx=0
Use the distributive property:
sinx(2cosx1)=0
Use the zero product property:
sinx=0 or 2cosx1=0
Solve both equations to sine or cosine:
sinx=0 or cosx=12
sinx=0 when x=0,π,2π
cosx=12 when x=π3 or x=2ππ3=5π3.
Answer x=0,π3,π,5π3,2π

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