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

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

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

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

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

Solution steps

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

Factor

tan (x) - 2 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

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

sin (θ) + cos (θ) = 2

sin^{2} (x) - cos^{2} (x) = \frac{1}{2}

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

sec (3 x) = \frac{2}{3}, 0 \leq x \leq 2 π

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