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

The general solution for sqrt(3)tan((2x)/3)+1=0 is x=(5pi)/4+(3pin)/2

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

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

x = \frac{5 π}{4} + \frac{3 πn}{2}

Solution steps

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

Move

1

to the right side

3 tan (\frac{2 x}{3}) = - 1

Divide both sides by

3

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

General solutions for

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

\frac{2 x}{3} = \frac{5 π}{6} + πn

Solve

\frac{2 x}{3} = \frac{5 π}{6} + πn : x = \frac{5 π}{4} + \frac{3 πn}{2}

x = \frac{5 π}{4} + \frac{3 πn}{2}

sin (x) = \frac{11}{61}

sin^{3} (x) = - sin^{2} (x)

cos (θ) = \frac{4}{5}, sin (θ)

3 cos (2 θ) - 3 cos (θ) + 3 = 4 cos (θ) + 10

cos (x) = \frac{1}{18}

What is the general solution for sqrt(3)tan((2x)/3)+1=0 ?
The general solution for sqrt(3)tan((2x)/3)+1=0 is x=(5pi)/4+(3pin)/2