What is the general solution for -cos(θ)-4=2cos^2(θ)-5 ?

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

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-cos(θ)-4=2cos^2(θ)-5

- cos (θ) - 4 = 2 cos^{2} (θ) - 5

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

Solution steps

- cos (θ) - 4 = 2 cos^{2} (θ) - 5

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - 1

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

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

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

3 cos^{2} (x) - cos (x) = 0

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

2 cos (θ) - 3 = - 2

2 sin (\frac{1}{2} x) = 1, 0^{\circ} \leq x \leq 1 2^{\circ}

2 sin (\frac{π}{4} + x) \cdot sin (\frac{π}{4} - x) + sin^{2} (x) = 0

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