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

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

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-cos(3x)=-cos(x)

- cos (3 x) = - cos (x)

x = πn, x = \frac{π}{2} + πn

Solution steps

- cos (3 x) = - cos (x)

Subtract

- cos (x)

from both sides

- cos (3 x) + cos (x) = 0

Rewrite using trig identities

2 sin (2 x) sin (x) = 0

Solving each part separately

sin (2 x) = 0 or sin (x) = 0

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

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

Merge Overlapping Intervals

x = πn, x = \frac{π}{2} + πn

2 sin (θ) cos (θ) - 2 cos (θ) = 0

4 sinh^{2} (x) = 0

- 2 cos (C) + 5 = 2 cos (C) + 4

2 cos^{2} (θ) + 2 sin (θ) - 12 = 9 sin (θ) - 7

2 csc^{2} (x) + cot^{2} (x) - 3 = 0

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