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

The general solution for 2cos(x/2)-sqrt(3)=0 is x= pi/3+4pin,x=(11pi)/3+4pin

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

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

x = \frac{π}{3} + 4 πn, x = \frac{11 π}{3} + 4 πn

Solution steps

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

Move

3

to the right side

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

Divide both sides by

2

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

General solutions for

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

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

Solve

\frac{x}{2} = \frac{π}{6} + 2 πn : x = \frac{π}{3} + 4 πn

Solve

\frac{x}{2} = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{3} + 4 πn

x = \frac{π}{3} + 4 πn, x = \frac{11 π}{3} + 4 πn

cos (2 x) + 3 cos (x) = 1

cos (2 θ) - cos (θ) = 2

sin (θ) - cos^{2} (θ) sin (θ) = - 1

5 sin (2 θ) - 2 sin (θ) = 0

2 cos (3 x) = 3

What is the general solution for 2cos(x/2)-sqrt(3)=0 ?
The general solution for 2cos(x/2)-sqrt(3)=0 is x= pi/3+4pin,x=(11pi)/3+4pin