What is the general solution for tan(2x-pi/6)= 1/(3^{1/2)} ?

The general solution for tan(2x-pi/6)= 1/(3^{1/2)} is x= pi/6+(pin)/2

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tan(2x-pi/6)= 1/(3^{1/2)}

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

x = \frac{π}{6} + \frac{πn}{2}

Solution steps

tan (2 x - \frac{π}{6}) = \frac{1}{3 ^{\frac{1}{2}}}

Apply trig inverse properties

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn

Solve

2 x - \frac{π}{6} = arctan (\frac{1}{3 ^{\frac{1}{2}}}) + πn : x = \frac{π}{6} + \frac{πn}{2}

x = \frac{π}{6} + \frac{πn}{2}

sin^{2} (\frac{x}{2}) - 1 = 0

69 = cos (x)

sin^{2} (θ) = cos (θ) + cos^{2} (θ)

7 cos (θ) = 2 + 9 cos (θ)

sec (x) \cdot cot (x) - 2 cot (x) + sec (x) = 2

What is the general solution for tan(2x-pi/6)= 1/(3^{1/2)} ?
The general solution for tan(2x-pi/6)= 1/(3^{1/2)} is x= pi/6+(pin)/2