What is the general solution for 2cos(1/2 x)-sqrt(3)=0 ?

The general solution for 2cos(1/2 x)-sqrt(3)=0 is x= pi/3+4pin,x=(11pi)/3+4pin

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2cos(1/2 x)-sqrt(3)=0

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

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

Solution steps

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

Move

3

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{1}{2} x = \frac{π}{6} + 2 πn, \frac{1}{2} x = \frac{11 π}{6} + 2 πn

Solve

\frac{1}{2} x = \frac{π}{6} + 2 πn : x = \frac{π}{3} + 4 πn

Solve

\frac{1}{2} x = \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

4 cos (θ) = 2

20 cos^{6} (x) - 57 cos^{4} (x) + 27 cos^{2} (x) = 0

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

2 + sin (x) = 5 sin (x)

2 cos (θ) + 5 = 0

What is the general solution for 2cos(1/2 x)-sqrt(3)=0 ?
The general solution for 2cos(1/2 x)-sqrt(3)=0 is x= pi/3+4pin,x=(11pi)/3+4pin