Find all solutions to the equation. \sqrt{3}\sin x-\sin2x=0

EunoR

EunoR

Answered question

2021-08-15

Find all solutions to the equation.
3sinxsin2x=0

Answer & Explanation

Szeteib

Szeteib

Skilled2021-08-16Added 102 answers

Given,
3sinxsin2x=0
And according to basic formula of trigonometry. sin(2x)=2sin(x)cos(x)
So we have
2sin(x)cos(x)=3sin(x)
We can cancel sin(x) from both sides which makes sin(x)=0 a solution i.e. 0, 180,360 etc.
2cos(x)=3 or cos(x)=32 giving x=30 and 330
So solutions in degrees in the range 0x<360 are 0,30,180 and 330 which shows there are four solutions for each 360 degrees range.
Answer:
x=2kπ or π6+2kπ or π+2kπ or 11π6+2kπ where k is integer.

Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-10Added 2605 answers

Answer is given below (on video)

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