What is the general solution for (sin(2x)-1)/3 =-1/6 ?

The general solution for (sin(2x)-1)/3 =-1/6 is x= pi/(12)+pin,x=(5pi)/(12)+pin

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(sin(2x)-1)/3 =-1/6

\frac{sin ( 2 x ) - 1}{3} = - \frac{1}{6}

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

Solution steps

\frac{sin ( 2 x ) - 1}{3} = - \frac{1}{6}

Multiply both sides by

3

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

Move

1

to the right side

sin (2 x) = \frac{1}{2}

General solutions for

sin (2 x) = \frac{1}{2}

2 x = \frac{π}{6} + 2 πn, 2 x = \frac{5 π}{6} + 2 πn

Solve

2 x = \frac{π}{6} + 2 πn : x = \frac{π}{12} + πn

Solve

2 x = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{12} + πn

x = \frac{π}{12} + πn, x = \frac{5 π}{12} + πn

2 sin^{2} (2 x) + cos (2 x) - 1 = 0

4 cos (x) + 2 = 3

sin (4 θ) = 4 sin (2 θ) cos (2 θ)

cos (x) = 6

6 sin (x) - 1 = 4 sin (x)

What is the general solution for (sin(2x)-1)/3 =-1/6 ?
The general solution for (sin(2x)-1)/3 =-1/6 is x= pi/(12)+pin,x=(5pi)/(12)+pin