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

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

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

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

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

Solution steps

3 cos (x) - 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) - 1 = - cos (x)

36 cos (2 x) = 0

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

sin (x) + cos (x) = 0, - π \leq x \leq π

cos (θ) = \frac{- 1}{2}, 0 \leq θ \leq 4 π

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