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

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

2 sin^{2} (x) - 5 sin (x) - 4 = 0

sin (θ) = 0.4815

6 cos^{2} (2 x) = sin (2 x) + 5

sin (A) = \frac{4}{5}, sin (2 A)

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= pi/3+pin,x= pi/6+2pin,x=(5pi)/6+2pin