What is the general solution for 2/(sqrt(3))cos(3x)=1 ?

The general solution for 2/(sqrt(3))cos(3x)=1 is x= pi/(18)+(2pin)/3 ,x=(11pi}{18}+\frac{2pin)/3

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2/(sqrt(3))cos(3x)=1

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

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

Solution steps

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

Simplify

\frac{2}{3} : \frac{2 3}{3}

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

Multiply both sides by

3

23 cos (3 x) = 3

Divide both sides by

23

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

General solutions for

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

3 x = \frac{π}{6} + 2 πn, 3 x = \frac{11 π}{6} + 2 πn

Solve

3 x = \frac{π}{6} + 2 πn : x = \frac{π}{18} + \frac{2 πn}{3}

Solve

3 x = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{18} + \frac{2 πn}{3}

x = \frac{π}{18} + \frac{2 πn}{3}, x = \frac{11 π}{18} + \frac{2 πn}{3}

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

csc^{2} (θ) + 5 = 7 - csc (θ)

3 tan^{2} (\frac{x}{3}) - 1 = 0

cos (x) = \frac{7}{10}

2 cos (2 x) + 3 = 2

What is the general solution for 2/(sqrt(3))cos(3x)=1 ?
The general solution for 2/(sqrt(3))cos(3x)=1 is x= pi/(18)+(2pin)/3 ,x=(11pi}{18}+\frac{2pin)/3