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

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

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

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

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

Solution steps

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

Move

1

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{1}{2} x = \frac{π}{3} + 2 πn, \frac{1}{2} x = \frac{5 π}{3} + 2 πn

Solve

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

Solve

\frac{1}{2} x = \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

2 cos (θ) sin (θ) - sin (θ) = 0

2 sin (x) cot (x) - cot (x) = - 1 + 2 sin (x)

sin (3 θ) = cos (3 θ)

2 + sec (x) = 0

cos (x) = \frac{3}{2}, sin (x), \frac{3 π}{2} \leq x \leq 2 π

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