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

The general solution for 2cos((2x)/3)-sqrt(3)=0 is x= pi/4+3pin,x=(11pi)/4+3pin

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

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

x = \frac{π}{4} + 3 πn, x = \frac{11 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{π}{6} + 2 πn, \frac{2 x}{3} = \frac{11 π}{6} + 2 πn

Solve

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

Solve

\frac{2 x}{3} = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{4} + 3 πn

x = \frac{π}{4} + 3 πn, x = \frac{11 π}{4} + 3 πn

- sin (2 x) - sin (x) = 0

sin^{2} (t) + 2 cos (t) = 1

6 tan (θ) - 2 cot (θ) = 0

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

2 sin^{2} (θ) + sin (θ) = 0, 0 \leq θ < 2 π

What is the general solution for 2cos((2x)/3)-sqrt(3)=0 ?
The general solution for 2cos((2x)/3)-sqrt(3)=0 is x= pi/4+3pin,x=(11pi)/4+3pin