What is the general solution for cot((2x)/3)=-sqrt(3) ?

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

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cot((2x)/3)=-sqrt(3)

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

x = \frac{5 π}{4} + \frac{3 πn}{2}

Solution steps

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

General solutions for

cot (\frac{2 x}{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) - 2 sin^{2} (x) = 0

sin (2 θ) + sin (θ) = 0, 0 \leq θ < 2 π

7 sin (x) = cos (x) - 4

5 sin^{2} (θ) - 11 sin (θ) + 2 = 0

tan^{2} (θ) + 3 sec (θ) = - 3

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