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

The general solution for 3sin(x)tan(x)+sqrt(3)sin(x)=0 is x=2pin,x=pi+2pin,x=(5pi)/6+pin

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3sin(x)tan(x)+sqrt(3)sin(x)=0

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

x = 2 πn, x = π + 2 πn, x = \frac{5 π}{6} + πn

Solution steps

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

Factor

3 sin (x) tan (x) + 3 sin (x) : sin (x) (3 tan (x) + 3)

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

3 tan (x) + 3 = 0 : x = \frac{5 π}{6} + πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{5 π}{6} + πn

sin (z) + cos (z) = 2

12 sin^{2} (t) + cos (t) - 4 = 2

- 3 tan (θ) - 11 = 3 tan (θ) - 6

cos^{2} (x) - 6 cos (x) - 1 = 0

tan (5 x) tan (x) = tan (5 x)

What is the general solution for 3sin(x)tan(x)+sqrt(3)sin(x)=0 ?
The general solution for 3sin(x)tan(x)+sqrt(3)sin(x)=0 is x=2pin,x=pi+2pin,x=(5pi)/6+pin