What is the general solution for sqrt(3)sin(x)=sin(x)tan(x) ?

The general solution for sqrt(3)sin(x)=sin(x)tan(x) is x=2pin,x=pi+2pin,x= pi/3+pin

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sqrt(3)sin(x)=sin(x)tan(x)

3 sin (x) = sin (x) tan (x)

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + πn

Solution steps

3 sin (x) = sin (x) tan (x)

Subtract

sin (x) tan (x)

from both sides

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

Factor

3 sin (x) - sin (x) tan (x) : sin (x) (3 - tan (x))

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

Solving each part separately

sin (x) = 0 or 3 - tan (x) = 0

sin (x) = 0 : x = 2 πn, x = π + 2 πn

3 - tan (x) = 0 : x = \frac{π}{3} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{3} + πn

- 2 sin (2 y) = 0

- 3 + 4 (cos^{2} (x))^{2} + 3 sin^{2} (x) = 0

4 sin (x - 3 0^{\circ}) - 1.3 = 0

2 cos (\frac{θ}{2}) = cos (θ) + 1

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

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