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

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

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-cos(θ)+cos(2θ)=0

- cos (θ) + cos (2 θ) = 0

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

Solution steps

- cos (θ) + cos (2 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}

cos (x) (cos (x) + 1) = 0

3 = 6 sin (θ)

sin (a) = \frac{1}{4}

33 sec (θ) + 4 = - 2

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

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