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

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

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

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

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

Solution steps

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

Factor

2 sin (x) tan (2 x) - 3 tan (2 x) : tan (2 x) (2 sin (x) - 3)

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

Solving each part separately

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

tan (2 x) = 0 : x = \frac{πn}{2}

2 sin (x) - 3 = 0 : x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn

Combine all the solutions

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

tan (x) = \frac{12}{8}

cos (2 t) - cos (t) = - 0.5, 0 \leq t \leq 2 π

3 ∣ sin (5 θ) ∣ = 0

4 cos (x) + 6 = 5 (cos (x) + 1)

cos (x) = 0.8736

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