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

The general solution for tan(x)cot(x)-sqrt(3)tan(x)=0 is x= pi/6+pin

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tan(x)cot(x)-sqrt(3)tan(x)=0

tan (x) cot (x) - 3 tan (x) = 0

x = \frac{π}{6} + πn

Solution steps

tan (x) cot (x) - 3 tan (x) = 0

Factor

tan (x) cot (x) - 3 tan (x) : tan (x) (cot (x) - 3)

tan (x) (cot (x) - 3) = 0

Solving each part separately

tan (x) = 0 or cot (x) - 3 = 0

tan (x) = 0 : x = πn

cot (x) - 3 = 0 : x = \frac{π}{6} + πn

Combine all the solutions

x = πn, x = \frac{π}{6} + πn

Since the equation is undefined for:

πn

x = \frac{π}{6} + πn

cos (θ) = 0.139

- \frac{2 3}{3} = sec (θ)

1 sin (3 0^{\circ}) = 1.7 sin (θ)

sin (x) = \pm \frac{1}{2}

30 = 211.49 - 20.96 cosh (0.03291765 x)

What is the general solution for tan(x)cot(x)-sqrt(3)tan(x)=0 ?
The general solution for tan(x)cot(x)-sqrt(3)tan(x)=0 is x= pi/6+pin