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

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

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-cos(θ)=-cos(2θ)

- cos (θ) = - cos (2 θ)

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

Solving each part separately

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

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

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

Combine all the solutions

θ = \frac{4 πn}{3}, θ = \frac{2 π}{3} + \frac{4 πn}{3}, θ = 4 πn, θ = 2 π + 4 πn

Merge Overlapping Intervals

θ = \frac{4 πn}{3}, θ = \frac{2 π}{3} + \frac{4 πn}{3}

cos (x) = \frac{4}{3.3 8 ^{2} + 4 ^{2}}

x, y = \frac{1}{π} arctan (\frac{x}{s}) + \frac{1}{2}

tan^{2} (θ) + 8 tan (θ) + 6 = 0

3 - sin (θ) = 5 sin (θ)

sin (x) + sin (2 x) = 0, 0 \leq x \leq 2 π

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