What is the general solution for 2+2cos(x)=6cos(x) ?

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

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2+2cos(x)=6cos(x)

2 + 2 cos (x) = 6 cos (x)

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

Solution steps

2 + 2 cos (x) = 6 cos (x)

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

120 = 120 sin (\frac{π}{3} c)

2 sin^{2} (x) + cos (x) - 3 = 0

cot (x) cos^{2} (x) = 2 cot (x), 0 \leq x \leq 2 π

2 cot^{2} (3 θ) = 5 csc (3 θ) - 4

1 - cos^{2} (\frac{x}{2}) = cos^{2} (x)

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