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

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

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

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

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

Solution steps

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

Factor

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

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

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

sin (θ) = \frac{( - \frac{2}{7} )}{2}

22 cos (θ) - 2 = 0

tan (x) = \frac{22}{326}

3 cos (6 x) = 2

2 cos (t) = 1 + sin (t)

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