What is the general solution for (tan(x)+sqrt(3))(2sin(x)-1)=0 ?

The general solution for (tan(x)+sqrt(3))(2sin(x)-1)=0 is x=(2pi)/3+pin,x= pi/6+2pin,x=(5pi)/6+2pin

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(tan(x)+sqrt(3))(2sin(x)-1)=0

(tan (x) + 3) (2 sin (x) - 1) = 0

x = \frac{2 π}{3} + πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

(tan (x) + 3) (2 sin (x) - 1) = 0

Solving each part separately

tan (x) + 3 = 0 or 2 sin (x) - 1 = 0

tan (x) + 3 = 0 : x = \frac{2 π}{3} + πn

2 sin (x) - 1 = 0 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{2 π}{3} + πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

2 cos (3 θ) + 1 = 0

cos (a) = - \frac{3}{5}

tan (x) = 3.5

sec (θ) = \frac{1}{sec ( θ )}

- 2 tan (θ) + 1 = 3 tan (θ) - 7

What is the general solution for (tan(x)+sqrt(3))(2sin(x)-1)=0 ?
The general solution for (tan(x)+sqrt(3))(2sin(x)-1)=0 is x=(2pi)/3+pin,x= pi/6+2pin,x=(5pi)/6+2pin