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

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

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

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

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

Solution steps

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

Switch sides

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}

cos (θ) = 0.6015

sin (θ) = \frac{- 4}{5}

θ, x = 5 sec (θ)

sec (3 x) - cos (3 0^{\circ}) = 0, \frac{x + 35}{5}

- 2 sin (x) + 3 = 0

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