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

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

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

1 + 3 tan (\frac{2 x - π}{3}) = 0

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

Solution steps

1 + 3 tan (\frac{2 x - π}{3}) = 0

Move

1

to the right side

3 tan (\frac{2 x - π}{3}) = - 1

Divide both sides by

3

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

General solutions for

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

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

Solve

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

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

tan (3 x) = tan (π x)

sin^{2} (2 x) = 0.5

sin (x) = - \frac{1}{2} 2

(6 cos (x) + 5 sin (x))^{2} + 11 sin^{2} (x) = 66

- 3 sin (B) - 2 = sin (B) - 2

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