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

The general solution for 2sin(3x-1)=sqrt(3) is x= 1/3+pi/9+(2pin)/3 ,x= 1/3+(2pi)/9+(2pin)/3

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2sin(3x-1)=sqrt(3)

2 sin (3 x - 1) = 3

x = \frac{1}{3} + \frac{π}{9} + \frac{2 πn}{3}, x = \frac{1}{3} + \frac{2 π}{9} + \frac{2 πn}{3}

Solution steps

2 sin (3 x - 1) = 3

Divide both sides by

2

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

General solutions for

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

3 x - 1 = \frac{π}{3} + 2 πn, 3 x - 1 = \frac{2 π}{3} + 2 πn

Solve

3 x - 1 = \frac{π}{3} + 2 πn : x = \frac{1}{3} + \frac{π}{9} + \frac{2 πn}{3}

Solve

3 x - 1 = \frac{2 π}{3} + 2 πn : x = \frac{1}{3} + \frac{2 π}{9} + \frac{2 πn}{3}

x = \frac{1}{3} + \frac{π}{9} + \frac{2 πn}{3}, x = \frac{1}{3} + \frac{2 π}{9} + \frac{2 πn}{3}

cos^{4} (x) - sin^{4} (x) = cos (2 x)

4 sin^{2} (x) - 3 = 0

sec (\frac{3 π}{2})

cot (2 π)

sin^{2} (0)

What is the general solution for 2sin(3x-1)=sqrt(3) ?
The general solution for 2sin(3x-1)=sqrt(3) is x= 1/3+pi/9+(2pin)/3 ,x= 1/3+(2pi)/9+(2pin)/3