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

The general solution for 2cos(3x)-sqrt(3)=0 is x= pi/(18)+(2pin)/3 ,x=(11pi}{18}+\frac{2pin)/3

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2cos(3x)-sqrt(3)=0

2 cos (3 x) - 3 = 0

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

Solution steps

2 cos (3 x) - 3 = 0

Move

3

to the right side

2 cos (3 x) = 3

Divide both sides by

2

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}

cos^{2} (x) - 8 cos (x) - 1 = 0

cos (x) + 2 = 1

2 cos (2 θ) = - 1

3 cot^{2} (x) = 3 cot (x)

sin (7 x) = \frac{3}{2}

What is the general solution for 2cos(3x)-sqrt(3)=0 ?
The general solution for 2cos(3x)-sqrt(3)=0 is x= pi/(18)+(2pin)/3 ,x=(11pi}{18}+\frac{2pin)/3