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

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

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2cos^2(θ)-cos(θ)-4=-6cos(θ)-6

2 cos^{2} (θ) - cos (θ) - 4 = - 6 cos (θ) - 6

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

Solution steps

2 cos^{2} (θ) - cos (θ) - 4 = - 6 cos (θ) - 6

Solve by substitution

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

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

cos (θ) = - 2 :

No Solution

Combine all the solutions

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

sin (x) + 2 cos (x) = 1

4 tan (2 x) - 4 cot (x) = 0

sin (x) = \frac{24}{25}

arcsin (3 x - π) = \frac{1}{2}

2 cos^{2} (θ) + sin (θ) - 1 = 0

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