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

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

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cos(θ)=-cos(2θ)

cos (θ) = - cos (2 θ)

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

Solution steps

cos (θ) = - cos (2 θ)

Subtract

- cos (2 θ)

from both sides

cos (θ) + cos (2 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}

3 (sin (x) - cos (x)) = 2 (sin (x) + cos (x))

\frac{sin ( 2 x )}{sin ( x )} = 1

θ, ma = t sin (θ) - m g

x, sin (x) - cos (y) - 2 = 0

\frac{cot ( a )}{cos ( a )} = cos (a)

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