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

The general solution for tan^2(x)+(sqrt(3)-1)tan(x)-sqrt(3)=0 is x= pi/4+pin,x=(2pi)/3+pin

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tan^2(x)+(sqrt(3)-1)tan(x)-sqrt(3)=0

tan^{2} (x) + (3 - 1) tan (x) - 3 = 0

x = \frac{π}{4} + πn, x = \frac{2 π}{3} + πn

Solution steps

tan^{2} (x) + (3 - 1) tan (x) - 3 = 0

Solve by substitution

tan (x) = 1, tan (x) = - 3

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = - 3 : x = \frac{2 π}{3} + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = \frac{2 π}{3} + πn

sin (θ) = \frac{2}{7}

2 sec (x) - 5 = 0

tan (a) + cot (a) = sec (a) cos (a)

- 5 tan^{2} (θ) + 3 = 8 tan (θ) + 6

cos (θ) = \frac{- 3}{13}

What is the general solution for tan^2(x)+(sqrt(3)-1)tan(x)-sqrt(3)=0 ?
The general solution for tan^2(x)+(sqrt(3)-1)tan(x)-sqrt(3)=0 is x= pi/4+pin,x=(2pi)/3+pin