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

The general solution for 3cot^2(x)-4cot(x)+sqrt(3)=0 is No Solution for x\in\mathbb{R}

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

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

No Solution for x \in R

Solution steps

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

Solve by substitution

cot (x) = \frac{2}{3} + i \frac{- 4 + 3 3}{3}, cot (x) = \frac{2}{3} - i \frac{- 4 + 3 3}{3}

cot (x) = \frac{2}{3} + i \frac{- 4 + 3 3}{3} :

No Solution

cot (x) = \frac{2}{3} - i \frac{- 4 + 3 3}{3} :

No Solution

Combine all the solutions

No Solution for x \in R

cos^{2} (x) + 5 cos (x) - 6 = 0

10 sin (x) = 4 cos^{2} (x) + 2

- 4 + sin (- 3 x + \frac{2 π}{3}) = - 4

2 \cdot sin (x) \cdot cos (x) = cos (x)

sin (2 θ) = \frac{- 2 6}{7}

What is the general solution for 3cot^2(x)-4cot(x)+sqrt(3)=0 ?
The general solution for 3cot^2(x)-4cot(x)+sqrt(3)=0 is No Solution for x\in\mathbb{R}