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

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

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

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

x = \frac{π}{6} + πn, x = \frac{2 π}{3} + πn

Solution steps

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

Solve by substitution

tan (x) = \frac{3}{3}, tan (x) = - 3

tan (x) = \frac{3}{3} : x = \frac{π}{6} + πn

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

Combine all the solutions

x = \frac{π}{6} + πn, x = \frac{2 π}{3} + πn

e^{\frac{- π}{t a n ( x )}} = 0.6

6 cos (2 x) = - 6 cos (x)

3 sec (2 θ) = 2

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

- 6 cos^{2} (θ) + cos (θ) + 7 = 5

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