What is the general solution for 2cos^2(θ)-4cos(θ)-1=-5cos(θ) ?

The general solution for 2cos^2(θ)-4cos(θ)-1=-5cos(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin

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2cos^2(θ)-4cos(θ)-1=-5cos(θ)

2 cos^{2} (θ) - 4 cos (θ) - 1 = - 5 cos (θ)

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

Solution steps

2 cos^{2} (θ) - 4 cos (θ) - 1 = - 5 cos (θ)

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

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

tan (x) = - 3 + 2

3 tan (x) - cot (x) = 0

sin^{2} (x) = \frac{( 2 m - 1 )}{4}

cos (2 x) - 0.25 = 0

What is the general solution for 2cos^2(θ)-4cos(θ)-1=-5cos(θ) ?
The general solution for 2cos^2(θ)-4cos(θ)-1=-5cos(θ) is θ= pi/3+2pin,θ=(5pi)/3+2pin,θ=pi+2pin