What is the general solution for sin(2x-pi/6)=-1/2 ?

The general solution for sin(2x-pi/6)=-1/2 is x=pin+(2pi)/3 ,x=pin+pi

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sin(2x-pi/6)=-1/2

sin (2 x - \frac{π}{6}) = - \frac{1}{2}

x = πn + \frac{2 π}{3}, x = πn + π

Solution steps

sin (2 x - \frac{π}{6}) = - \frac{1}{2}

General solutions for

sin (2 x - \frac{π}{6}) = - \frac{1}{2}

2 x - \frac{π}{6} = \frac{7 π}{6} + 2 πn, 2 x - \frac{π}{6} = \frac{11 π}{6} + 2 πn

Solve

2 x - \frac{π}{6} = \frac{7 π}{6} + 2 πn : x = πn + \frac{2 π}{3}

Solve

2 x - \frac{π}{6} = \frac{11 π}{6} + 2 πn : x = πn + π

x = πn + \frac{2 π}{3}, x = πn + π

cos (x) (2 sin (x) + 3) = 0

cot (θ) + 2 csc (θ) = 4

9 sin^{2} (x) - 3 sin (x) = cos^{2} (x)

tan (x) + 1 = - 3 - 3 cot (x)

0 = a sin (x) + b cos (x)

What is the general solution for sin(2x-pi/6)=-1/2 ?
The general solution for sin(2x-pi/6)=-1/2 is x=pin+(2pi)/3 ,x=pin+pi