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

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

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

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

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

Solution steps

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

Factor

2 tan (x) sin (x) - tan (x) : tan (x) (2 sin (x) - 1)

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

Solving each part separately

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

tan (x) = 0 : x = πn

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

Combine all the solutions

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

tan (\frac{x}{2}) = 5

- 6 cos (2 x) + 23 cos (x) - 11 = 0

sin^{2} (x + 4) = 1

\frac{178.9}{sin ( 12 5 ^{\circ} )} = \frac{125}{sin ( x )}

cos (θ) = \frac{3}{8}

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