What is the general solution for 1sin(x)tan(x)+sqrt(3)sin(x)=0 ?

The general solution for 1sin(x)tan(x)+sqrt(3)sin(x)=0 is x=2pin,x=pi+2pin,x=(2pi)/3+pin

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1sin(x)tan(x)+sqrt(3)sin(x)=0

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

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

Solution steps

1 \cdot sin (x) tan (x) + 3 sin (x) = 0

Factor

1 \cdot sin (x) tan (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{2 π}{3} + πn

Combine all the solutions

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

6 (sin (x))^{2} - 13 cos (x) = 11

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

tan^{2} (x) + 2 + 2 tan (x) - 7 = 0

(2 cos (x) + 1) = 0

3 cos (x) + 2 = 0

What is the general solution for 1sin(x)tan(x)+sqrt(3)sin(x)=0 ?
The general solution for 1sin(x)tan(x)+sqrt(3)sin(x)=0 is x=2pin,x=pi+2pin,x=(2pi)/3+pin