What is the general solution for cos(3θ)=cos(θ) ?

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

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cos(3θ)=cos(θ)

cos (3 θ) = cos (θ)

θ = πn, θ = \frac{π}{2} + πn

Solution steps

cos (3 θ) = cos (θ)

Subtract

cos (θ)

from both sides

cos (3 θ) - cos (θ) = 0

Rewrite using trig identities

- 2 sin (2 θ) sin (θ) = 0

Solving each part separately

sin (2 θ) = 0 or sin (θ) = 0

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

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

Combine all the solutions

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

Merge Overlapping Intervals

θ = πn, θ = \frac{π}{2} + πn

(tan (x) - sec (x))^{2} = 3

y, ln (x^{2} + 10) + csc (y) = c

sin (a) = \frac{7}{15}

\frac{3 3}{14} = sin (x)

6 cos (x) = 2 + 2 cos (x)

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