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

The general solution for 2cos(x/2)+sqrt(3)=0 is x=(5pi)/3+4pin,x=(7pi)/3+4pin

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2cos(x/2)+sqrt(3)=0

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

x = \frac{5 π}{3} + 4 πn, x = \frac{7 π}{3} + 4 πn

Solution steps

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

Move

3

to the right side

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{5 π}{6} + 2 πn, \frac{x}{2} = \frac{7 π}{6} + 2 πn

Solve

\frac{x}{2} = \frac{5 π}{6} + 2 πn : x = \frac{5 π}{3} + 4 πn

Solve

\frac{x}{2} = \frac{7 π}{6} + 2 πn : x = \frac{7 π}{3} + 4 πn

x = \frac{5 π}{3} + 4 πn, x = \frac{7 π}{3} + 4 πn

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

25 sin (x) cos (x) - 5 sin (x) + 20 cos (x) = 4

sin (θ) = - 0.9

cos (2 T) = 1, 0 \leq T \leq 2 π

2 - 2 cos^{2} (\frac{x}{2}) = 2 cos^{2} (x)

What is the general solution for 2cos(x/2)+sqrt(3)=0 ?
The general solution for 2cos(x/2)+sqrt(3)=0 is x=(5pi)/3+4pin,x=(7pi)/3+4pin