What is the general solution for sqrt(3)cot^2(x)-4cot(x)+sqrt(3)=0 ?

The general solution for sqrt(3)cot^2(x)-4cot(x)+sqrt(3)=0 is x= pi/6+pin,x= pi/3+pin

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sqrt(3)cot^2(x)-4cot(x)+sqrt(3)=0

3 cot^{2} (x) - 4 cot (x) + 3 = 0

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

Solution steps

3 cot^{2} (x) - 4 cot (x) + 3 = 0

Solve by substitution

cot (x) = 3, cot (x) = \frac{3}{3}

cot (x) = 3 : x = \frac{π}{6} + πn

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

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{π}{3} + πn

cot (θ) + tan (θ) = 2

3 cos^{2} (θ) - 1 = 0

sin (3 x - \frac{π}{6}) = - cos (3 x - \frac{π}{6})

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

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

What is the general solution for sqrt(3)cot^2(x)-4cot(x)+sqrt(3)=0 ?
The general solution for sqrt(3)cot^2(x)-4cot(x)+sqrt(3)=0 is x= pi/6+pin,x= pi/3+pin