What is the general solution for cos(5x)=cos(3x) ?

The general solution for cos(5x)=cos(3x) is x=(pin)/2 ,x= pi/4+(pin)/2 ,x=2pin,x=pi+2pin

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cos(5x)=cos(3x)

cos (5 x) = cos (3 x)

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

Solution steps

cos (5 x) = cos (3 x)

Subtract

cos (3 x)

from both sides

cos (5 x) - cos (3 x) = 0

Rewrite using trig identities

- 2 sin (4 x) sin (x) = 0

Solving each part separately

sin (4 x) = 0 or sin (x) = 0

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

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

2 cos (2 t) = 0

4 cos^{2} (θ) = 3 + 3 sin (θ)

4 cos (3 θ) + 23 = 0

cos (2 θ) + 3 cos (θ) - 1 = 0

2 sin^{2} (x) = 2 - 3 cos (x)

What is the general solution for cos(5x)=cos(3x) ?
The general solution for cos(5x)=cos(3x) is x=(pin)/2 ,x= pi/4+(pin)/2 ,x=2pin,x=pi+2pin