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

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

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

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

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

Solution steps

3 sin (x) - sin (2 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

7 cos^{2} (x) + 14 cos (x) + 7 = 0

θ, 2 sin (θ) = 2 cos (2 θ)

sec (θ) + 4 = 4 sec (θ)

sin (2 x) - 4 \cdot cos (x) = 0

5 tan (θ) + 3 = 0

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