What is the general solution for cos(6x)=cos(2x) ?

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

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cos(6x)=cos(2x)

cos (6 x) = cos (2 x)

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

Solution steps

cos (6 x) = cos (2 x)

Subtract

cos (2 x)

from both sides

cos (6 x) - cos (2 x) = 0

Rewrite using trig identities

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

Solving each part separately

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

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

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

Combine all the solutions

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

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

cos^{4} (x) + cos^{3} (x) - 2 = 0

tan^{2} (x) = \frac{1}{cos ( x ) + 1}

\frac{sin ^{2} ( x ) - 2 cos ( x ) + 1}{4} = 0

cos^{2} (x) + cos^{4} (x) + cos^{6} (x) = 0

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