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

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

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cos(2θ)-2cos(θ)=-1

cos (2 θ) - 2 cos (θ) = - 1

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

Solution steps

cos (2 θ) - 2 cos (θ) = - 1

Subtract

- 1

from both sides

cos (2 θ) - 2 cos (θ) + 1 = 0

Rewrite using trig identities

- 2 cos (θ) + 2 cos^{2} (θ) = 0

Solve by substitution

cos (θ) = 1, cos (θ) = 0

cos (θ) = 1 : θ = 2 πn

cos (θ) = 0 : θ = \frac{π}{2} + 2 πn, θ = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

(sec (x) - 2) (3 sec (x) + 2) = 0

csc (x) cot (x) = 2

2 sin^{2} (x) = 2 + cos (2 x)

2 tan^{2} (x) - sec (x) = 1

2 cos (x) = 2 sin (x)

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