What is the general solution for 5cos(x)-sqrt(3)=3cos(x) ?

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

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5cos(x)-sqrt(3)=3cos(x)

5 cos (x) - 3 = 3 cos (x)

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

Solution steps

5 cos (x) - 3 = 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

tan (x) + 3 = 0

2 sin (x) - 1 = 0

tan (x) = \frac{5}{3}

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

2 sin (x) + csc (x) = 3

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