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

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

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cos(2θ)=-cos(θ)

cos (2 θ) = - cos (θ)

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

Solution steps

cos (2 θ) = - cos (θ)

Subtract

- cos (θ)

from both sides

cos (2 θ) + cos (θ) = 0

Rewrite using trig identities

2 cos (\frac{3 θ}{2}) cos (\frac{θ}{2}) = 0

Solving each part separately

cos (\frac{3 θ}{2}) = 0 or cos (\frac{θ}{2}) = 0

cos (\frac{3 θ}{2}) = 0 : θ = \frac{π}{3} + \frac{4 πn}{3}, θ = π + \frac{4 πn}{3}

cos (\frac{θ}{2}) = 0 : θ = π + 4 πn, θ = 3 π + 4 πn

Combine all the solutions

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

Merge Overlapping Intervals

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

2 sin (x) cos (x) - 2 cos (x) - sin (x) + 1 = 0

2 cos^{2} (θ) = 1 - cos (θ)

- 5 cos^{2} (θ) = 12 sin (θ) + 4

cos^{2} (t) - 2 sin (t) - 1 = 0

cos (2 x) + 8 sin^{2} (x) = 4

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