What is the general solution for 2cos(2θ)=6cos(θ)-4 ?

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

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2cos(2θ)=6cos(θ)-4

2 cos (2 θ) = 6 cos (θ) - 4

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

Solution steps

2 cos (2 θ) = 6 cos (θ) - 4

Subtract

6 cos (θ) - 4

from both sides

2 cos (2 θ) - 6 cos (θ) + 4 = 0

Rewrite using trig identities

2 + 4 cos^{2} (θ) - 6 cos (θ) = 0

Solve by substitution

cos (θ) = 1, cos (θ) = \frac{1}{2}

cos (θ) = 1 : θ = 2 πn

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

Combine all the solutions

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

5 sin (θ) - 4 = 2 sin (θ) - 6

cos (2 θ) - cos (4 θ) = 0

tan (x) = 1.4

sin (θ) = 0.71

2 tan^{2} (x) - 3 tan (x) + 1 = 0

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