What is the general solution for cos(4x)-cos(2x)=0 ?

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

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

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

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

Solution steps

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

Rewrite using trig identities

- 2 sin (3 x) sin (x) = 0

Solving each part separately

sin (3 x) = 0 or sin (x) = 0

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

Combine all the solutions

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

Merge Overlapping Intervals

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

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

2 cos (θ) = - 2

tan (\frac{x}{3}) = 3

cos (\frac{x}{2}) - 1 = 0

cos (2 x) + 1 = 0

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