What is the general solution for sin(2x)-sqrt(3)sin(x)=0 ?

The general solution for sin(2x)-sqrt(3)sin(x)=0 is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(11pi)/6+2pin

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sin(2x)-sqrt(3)sin(x)=0

sin (2 x) - 3 sin (x) = 0

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

sin (2 x) - 3 sin (x) = 0

Rewrite using trig identities

- sin (x) 3 + 2 cos (x) sin (x) = 0

Factor

- sin (x) 3 + 2 cos (x) sin (x) : sin (x) (- 3 + 2 cos (x))

sin (x) (- 3 + 2 cos (x)) = 0

Solving each part separately

sin (x) = 0 or - 3 + 2 cos (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

- 3 + 2 cos (x) = 0 : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

2 sin (2 x) + 3 cos (x) = 0

\frac{1}{2} + cos (x) = 0

- 63 cot (θ) + 1 = - 5

5 - 10 sin (2 x) = 0

x, cos (3 x) = 0

What is the general solution for sin(2x)-sqrt(3)sin(x)=0 ?
The general solution for sin(2x)-sqrt(3)sin(x)=0 is x=2pin,x=pi+2pin,x= pi/6+2pin,x=(11pi)/6+2pin