What is the general solution for -6cos^2(θ)-9cos(θ)-7=8cos(θ) ?

The general solution for -6cos^2(θ)-9cos(θ)-7=8cos(θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin

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-6cos^2(θ)-9cos(θ)-7=8cos(θ)

- 6 cos^{2} (θ) - 9 cos (θ) - 7 = 8 cos (θ)

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Solution steps

- 6 cos^{2} (θ) - 9 cos (θ) - 7 = 8 cos (θ)

Solve by substitution

cos (θ) = - \frac{7}{3}, cos (θ) = - \frac{1}{2}

cos (θ) = - \frac{7}{3} :

No Solution

cos (θ) = - \frac{1}{2} : θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

Combine all the solutions

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

θ, 1 + cos (θ) = 1 - sin (θ)

sin (x) = 1

2 tan^{2} (θ) - tan (θ) = 0

3 sin (θ) + 2 = 0

7 cos (2 θ) = 7 cos (θ)

What is the general solution for -6cos^2(θ)-9cos(θ)-7=8cos(θ) ?
The general solution for -6cos^2(θ)-9cos(θ)-7=8cos(θ) is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin