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

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

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

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

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

Solution steps

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

tan (x) (cot (x) - \frac{3}{3}) = 0

24 sin^{2} (x) = 24 - 12 cos (x)

3 tan (x) = 1

2 cos^{2} (t) + 3 cos (t) + 1 = 0

cos (x) = - \frac{1}{5}

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