What is the general solution for 4cos(θ)+sqrt(3)=2cos(θ) ?

The general solution for 4cos(θ)+sqrt(3)=2cos(θ) is θ=(5pi)/6+2pin,θ=(7pi)/6+2pin

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4cos(θ)+sqrt(3)=2cos(θ)

4 cos (θ) + 3 = 2 cos (θ)

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

Solution steps

4 cos (θ) + 3 = 2 cos (θ)

Solve by substitution

cos (θ) = - \frac{3}{2}

cos (θ) = - \frac{3}{2} : θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

Combine all the solutions

θ = \frac{5 π}{6} + 2 πn, θ = \frac{7 π}{6} + 2 πn

sin (2 x) = \frac{1}{2}, 0 \leq x < 2 π

6 cos^{2} (θ) - cos (θ) - 1 = 0

11 tan (x) + 6 = 3 tan (x) + 6

∣ cos (3 x) ∣ = \frac{1}{2}

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

What is the general solution for 4cos(θ)+sqrt(3)=2cos(θ) ?
The general solution for 4cos(θ)+sqrt(3)=2cos(θ) is θ=(5pi)/6+2pin,θ=(7pi)/6+2pin