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

The general solution for 2cos(x/2)-1=0 is x=(2pi)/3+4pin,x=(10pi)/3+4pin

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2cos(x/2)-1=0

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

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

Solution steps

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

Move

1

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{x}{2} = \frac{π}{3} + 2 πn, \frac{x}{2} = \frac{5 π}{3} + 2 πn

Solve

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

Solve

\frac{x}{2} = \frac{5 π}{3} + 2 πn : x = \frac{10 π}{3} + 4 πn

x = \frac{2 π}{3} + 4 πn, x = \frac{10 π}{3} + 4 πn

5 cos^{2} (x) - 6 cos (x) + 1 = 0

1 + sec^{2} (x) = tan^{2} (x)

cos (t) = \frac{1}{2}

3 cos^{2} (x) + 8 sin (x) = 7

csc (x + 1 0^{\circ}) = 3

What is the general solution for 2cos(x/2)-1=0 ?
The general solution for 2cos(x/2)-1=0 is x=(2pi)/3+4pin,x=(10pi)/3+4pin