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

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

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cos(3x)=-cos(x)

cos (3 x) = - cos (x)

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

Solving each part separately

cos (2 x) = 0 or cos (x) = 0

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

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

Combine all the solutions

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

3 sin (x) - ((3 sin (x)) - 1) = 1 n

3 = 3 - 3 cos (θ)

a, tan (a) - tan (b) = 0

cos (x) = - cos (\frac{π}{7})

5 cos (x) - sin (x) = 1

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