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

The general solution for cos(x)-cos(x/2)=0 is x=(8pin)/3 ,x=(4pi)/3+(8pin)/3

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

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

x = \frac{8 πn}{3}, x = \frac{4 π}{3} + \frac{8 πn}{3}

Solution steps

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

Rewrite using trig identities

- 2 sin (\frac{3 x}{4}) sin (\frac{x}{4}) = 0

Solving each part separately

sin (\frac{3 x}{4}) = 0 or sin (\frac{x}{4}) = 0

sin (\frac{3 x}{4}) = 0 : x = \frac{8 πn}{3}, x = \frac{4 π}{3} + \frac{8 πn}{3}

sin (\frac{x}{4}) = 0 : x = 8 πn, x = 4 π + 8 πn

Combine all the solutions

x = \frac{8 πn}{3}, x = \frac{4 π}{3} + \frac{8 πn}{3}, x = 8 πn, x = 4 π + 8 πn

Merge Overlapping Intervals

x = \frac{8 πn}{3}, x = \frac{4 π}{3} + \frac{8 πn}{3}

sin (x) = 0, - \frac{π}{4} < x < \frac{9 π}{4}

2 tan (x) cos (x) = tan (x)

sin (x) = \frac{5}{4}

sin (2 θ) = 3 cos (θ)

x, tan (x) + ∣ tan (x) ∣ = 1

What is the general solution for cos(x)-cos(x/2)=0 ?
The general solution for cos(x)-cos(x/2)=0 is x=(8pin)/3 ,x=(4pi)/3+(8pin)/3