What is the general solution for cos(3x)-cos(5x)=0 ?

The general solution for cos(3x)-cos(5x)=0 is x=(pin)/2 ,x= pi/4+(pin)/2 ,x=2pin,x=pi+2pin

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

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

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

Solution steps

cos (3 x) - cos (5 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 = 2 cos (x)

4 cos (x) = 4 cos (2 x)

cos (θ) = 513, 3 π^{2} < θ < 2 π

cos (x) + ∣ cos (x) ∣ = 1

2 sin (\frac{π}{3} - x) = 1

What is the general solution for cos(3x)-cos(5x)=0 ?
The general solution for cos(3x)-cos(5x)=0 is x=(pin)/2 ,x= pi/4+(pin)/2 ,x=2pin,x=pi+2pin