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

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

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solvefor x,cos(2x)-cos(x)=0

solve for

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

x = \frac{4 πn}{3}, x = \frac{2 π}{3} + \frac{4 πn}{3}

Solution steps

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

Rewrite using trig identities

- 2 sin (\frac{3 x}{2}) sin (\frac{x}{2}) = 0

Solving each part separately

sin (\frac{3 x}{2}) = 0 or sin (\frac{x}{2}) = 0

sin (\frac{3 x}{2}) = 0 : x = \frac{4 πn}{3}, x = \frac{2 π}{3} + \frac{4 πn}{3}

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

Combine all the solutions

x = \frac{4 πn}{3}, x = \frac{2 π}{3} + \frac{4 πn}{3}, x = 4 πn, x = 2 π + 4 πn

Merge Overlapping Intervals

x = \frac{4 πn}{3}, x = \frac{2 π}{3} + \frac{4 πn}{3}

tan^{2} (x) + 2 tan (x) - 1 = 0

sin (3 x) = \frac{1}{2}, 0 \leq x \leq 2 π

x, sin (x + y) + sin (x - y) = 1

cos (2 x) = sin (x - \frac{π}{4})

sin (2 x + 60) + sin (x + 30) = 0, 0 \leq x \leq 2 π

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