What is the general solution for (5sqrt(3))/3 cos(x)=1+sqrt(3)cos(x) ?

The general solution for (5sqrt(3))/3 cos(x)=1+sqrt(3)cos(x) is x= pi/6+2pin,x=(11pi)/6+2pin

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(5sqrt(3))/3 cos(x)=1+sqrt(3)cos(x)

\frac{5 3}{3} cos (x) = 1 + 3 cos (x)

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

Solution steps

\frac{5 3}{3} cos (x) = 1 + 3 cos (x)

Solve by substitution

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

cos (x) = \frac{3}{2} : x = \frac{π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

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

sin (x) n = 3

3 cos (2 x) = 4 - 11 cos (x)

x, 2 cos^{2} (x) - cos (x) = 0

8 tan (2 x) - 5 = 3

- 8 cos (x) = 3

What is the general solution for (5sqrt(3))/3 cos(x)=1+sqrt(3)cos(x) ?
The general solution for (5sqrt(3))/3 cos(x)=1+sqrt(3)cos(x) is x= pi/6+2pin,x=(11pi)/6+2pin