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

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

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

solve for

x, cos (x) = cos (2 x)

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

Solution steps

cos (x) = cos (2 x)

Subtract

cos (2 x)

from both sides

cos (x) - cos (2 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}

cos (x) = 0.50074242

2 sin (4 x) - 1 = 0, - 2 π \leq x \leq 3 π

tan (θ) = \frac{10}{10}

0 = sin (\frac{θ}{2}) - sin (θ)

sin (b) = 0.823

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