What is the general solution for tan^2(x+pi/6)=3 ?

The general solution for tan^2(x+pi/6)=3 is x=pin+pi/6 ,x=pin+pi/2

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tan^2(x+pi/6)=3

tan^{2} (x + \frac{π}{6}) = 3

x = πn + \frac{π}{6}, x = πn + \frac{π}{2}

Solution steps

tan^{2} (x + \frac{π}{6}) = 3

Solve by substitution

tan (x + \frac{π}{6}) = 3, tan (x + \frac{π}{6}) = - 3

tan (x + \frac{π}{6}) = 3 : x = πn + \frac{π}{6}

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

Combine all the solutions

x = πn + \frac{π}{6}, x = πn + \frac{π}{2}

cos (θ) cos (2 θ) + sin (θ) sin (2 θ) = \frac{3}{2}

3 cos (2 x) - 2 cos (x) - 1 = 0

sin (3 π x) = 0

tan (2 t) = 1, 0 \leq t < 2 π

sin^{2} (x) = cot (x)

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