What is the general solution for tan^2(x)+1/6+(tan(1))/3 =0 ?

The general solution for tan^2(x)+1/6+(tan(1))/3 =0 is No Solution for x\in\mathbb{R}

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tan^2(x)+1/6+(tan(1))/3 =0

tan^{2} (x) + \frac{1}{6} + \frac{tan ( 1 )}{3} = 0

No Solution for x \in R

Solution steps

tan^{2} (x) + \frac{1}{6} + \frac{tan ( 1 )}{3} = 0

Solve by substitution

tan (x) = i \frac{1 + 2 tan ( 1 )}{6}, tan (x) = - i \frac{1 + 2 tan ( 1 )}{6}

tan (x) = i \frac{1 + 2 tan ( 1 )}{6} :

No Solution

tan (x) = - i \frac{1 + 2 tan ( 1 )}{6} :

No Solution

Combine all the solutions

No Solution for x \in R

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

3 - 4 sin^{3} (x) = sin^{3} (x)

cos^{4} (x) = \frac{3}{8} + \frac{1}{2} cos^{2} (x) + \frac{1}{8} cos^{4} (x)

sin (2 x) = 5 cos (x)

sin (a) = 0.4848

What is the general solution for tan^2(x)+1/6+(tan(1))/3 =0 ?
The general solution for tan^2(x)+1/6+(tan(1))/3 =0 is No Solution for x\in\mathbb{R}