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

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

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

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

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

Solution steps

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

Move

3

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{2 x}{3} = \frac{5 π}{6} + 2 πn, \frac{2 x}{3} = \frac{7 π}{6} + 2 πn

Solve

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

Solve

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

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

sin^{2} (x) - 7 cos (x) - 7 = 0

3 sin^{2} (x) = sin (x)

2 cos (2 θ) - 3 cos (θ) + 12 = 5 cos (θ) + 7

sin (4 x) - sin (x) = 0

tan (θ) = \frac{7}{5}

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