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

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

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cos(2θ)-cos(θ)=0

cos (2 θ) - cos (θ) = 0

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

Solution steps

cos (2 θ) - cos (θ) = 0

Rewrite using trig identities

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

Solving each part separately

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

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

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

Combine all the solutions

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

Merge Overlapping Intervals

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

cot (x) + 3 = 0

4 sin^{2} (θ) + 4 = 5

sec^{2} (x) - 6 tan (x) = - 4

64 cos^{2} (x) - 16 = 0

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

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