What is the general solution for 3/(1+cos(θ))=1+2cos(θ) ?

The general solution for 3/(1+cos(θ))=1+2cos(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin

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3/(1+cos(θ))=1+2cos(θ)

\frac{3}{1 + cos ( θ )} = 1 + 2 cos (θ)

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

Solution steps

\frac{3}{1 + cos ( θ )} = 1 + 2 cos (θ)

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - 2

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

cos (θ) = - 2 :

No Solution

Combine all the solutions

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

4 - 4 cos (θ) = 6

sin^{2} (θ) - 2 sin (θ) + 1 = 0

cos (4 θ) = - \frac{1}{2}

sin (x) = \frac{2 5}{5}

(2 cos (x) - 1) (sin (x) - 1) = 0

What is the general solution for 3/(1+cos(θ))=1+2cos(θ) ?
The general solution for 3/(1+cos(θ))=1+2cos(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin