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

The general solution for sqrt(3)tan(2x)+1=0 is x=(5pi}{12}+\frac{pin)/2

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

3 tan (2 x) + 1 = 0

x = \frac{5 π}{12} + \frac{πn}{2}

Solution steps

3 tan (2 x) + 1 = 0

Move

1

to the right side

3 tan (2 x) = - 1

Divide both sides by

3

tan (2 x) = - \frac{3}{3}

General solutions for

tan (2 x) = - \frac{3}{3}

2 x = \frac{5 π}{6} + πn

Solve

2 x = \frac{5 π}{6} + πn : x = \frac{5 π}{12} + \frac{πn}{2}

x = \frac{5 π}{12} + \frac{πn}{2}

sin (x) = \frac{2}{π}

sin (2 x) cos (x) + cos (2 x) sin (x) = \frac{2}{2}

sin (2 x) = 3 sin (x)

csc (θ) = - 2

4 cos^{2} (x) - 1 = 0, 0 < x < 2 π

What is the general solution for sqrt(3)tan(2x)+1=0 ?
The general solution for sqrt(3)tan(2x)+1=0 is x=(5pi}{12}+\frac{pin)/2