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

The general solution for 2cos(x/2)+1=0 is x=(4pi)/3+4pin,x=(8pi)/3+4pin

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2cos(x/2)+1=0

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

x = \frac{4 π}{3} + 4 πn, x = \frac{8 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{2 π}{3} + 2 πn, \frac{x}{2} = \frac{4 π}{3} + 2 πn

Solve

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

Solve

\frac{x}{2} = \frac{4 π}{3} + 2 πn : x = \frac{8 π}{3} + 4 πn

x = \frac{4 π}{3} + 4 πn, x = \frac{8 π}{3} + 4 πn

- tan (2 θ) + 2 sin (θ) = 0

- 3 cos^{2} (θ) + 6 = sin (θ) + 5

cos^{2} (θ) + 4 cos (θ) = 0

2 sin (x) = 2

tan (θ) = \frac{- 1}{3}

What is the general solution for 2cos(x/2)+1=0 ?
The general solution for 2cos(x/2)+1=0 is x=(4pi)/3+4pin,x=(8pi)/3+4pin