What is the general solution for 2cos(3x)-1=0 ?

The general solution for 2cos(3x)-1=0 is x= pi/9+(2pin)/3 ,x=(5pi)/9+(2pin)/3

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2cos(3x)-1=0

2 cos (3 x) - 1 = 0

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{5 π}{9} + \frac{2 πn}{3}

Solution steps

2 cos (3 x) - 1 = 0

Move

1

to the right side

2 cos (3 x) = 1

Divide both sides by

2

cos (3 x) = \frac{1}{2}

General solutions for

cos (3 x) = \frac{1}{2}

3 x = \frac{π}{3} + 2 πn, 3 x = \frac{5 π}{3} + 2 πn

Solve

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

Solve

3 x = \frac{5 π}{3} + 2 πn : x = \frac{5 π}{9} + \frac{2 πn}{3}

x = \frac{π}{9} + \frac{2 πn}{3}, x = \frac{5 π}{9} + \frac{2 πn}{3}

3 csc (θ) + 2 = 0

- sin (\frac{π}{4})

tan^{2} (x) - tan (x) = 0

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

2 sin (2 θ) = 1

What is the general solution for 2cos(3x)-1=0 ?
The general solution for 2cos(3x)-1=0 is x= pi/9+(2pin)/3 ,x=(5pi)/9+(2pin)/3