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

The general solution for 2cos(x/3)-sqrt(3)=0 is x= pi/2+6pin,x=(11pi)/2+6pin

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

2 cos (\frac{x}{3}) - 3 = 0

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

Solution steps

2 cos (\frac{x}{3}) - 3 = 0

Move

3

to the right side

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

Divide both sides by

2

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

General solutions for

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

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

Solve

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

Solve

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

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

2 csc^{2} (x) + 3 csc (x) - 2 = 0

2 sin^{2} (x) + 3 sin (x) + 1 = 0

cos (\frac{17 π}{6})

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

cos (- \frac{π}{2})

What is the general solution for 2cos(x/3)-sqrt(3)=0 ?
The general solution for 2cos(x/3)-sqrt(3)=0 is x= pi/2+6pin,x=(11pi)/2+6pin