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

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

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tan((2x)/3)-sqrt(3)=0

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

x = \frac{π}{2} + \frac{3 πn}{2}

Solution steps

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

Move

3

to the right side

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

General solutions for

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

\frac{2 x}{3} = \frac{π}{3} + πn

Solve

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

x = \frac{π}{2} + \frac{3 πn}{2}

2 sin^{2} (x) - cos^{2} (x) - 2 = 0

cos (3 x) \cdot 3 = 0

16 sec^{2} (θ) - 25 = 0

2 csc^{2} (x) - 4 = 0

2 sin^{2} (θ) - 3 sin (θ) - 2 = 0, 0 \leq θ \leq 2 π

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