What is the general solution for cos(4x)=cos(8x) ?

The general solution for cos(4x)=cos(8x) is x=pin,x= pi/2+pin,x=(pin)/3 ,x= pi/6+(pin)/3

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cos(4x)=cos(8x)

cos (4 x) = cos (8 x)

x = πn, x = \frac{π}{2} + πn, x = \frac{πn}{3}, x = \frac{π}{6} + \frac{πn}{3}

Solution steps

cos (4 x) = cos (8 x)

Subtract

cos (8 x)

from both sides

cos (4 x) - cos (8 x) = 0

Rewrite using trig identities

2 sin (2 x) sin (6 x) = 0

Solving each part separately

sin (2 x) = 0 or sin (6 x) = 0

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

sin (6 x) = 0 : x = \frac{πn}{3}, x = \frac{π}{6} + \frac{πn}{3}

Combine all the solutions

x = πn, x = \frac{π}{2} + πn, x = \frac{πn}{3}, x = \frac{π}{6} + \frac{πn}{3}

cos (2 x) - cos (x) = 2

4 sin (2 x) + 23 = 0

x, 3 = 18 cos (x)

x, 2 sin (\frac{π ( x - 2 )}{6}) = 1

(1 - sin (x)) (1 - sin (x)) = cos^{2} (x)

What is the general solution for cos(4x)=cos(8x) ?
The general solution for cos(4x)=cos(8x) is x=pin,x= pi/2+pin,x=(pin)/3 ,x= pi/6+(pin)/3