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

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

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cos(θ)+cos(2θ)=0

cos (θ) + cos (2 θ) = 0

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

Solution steps

cos (θ) + cos (2 θ) = 0

Rewrite using trig identities

2 cos (\frac{3 θ}{2}) cos (\frac{θ}{2}) = 0

Solving each part separately

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

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

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

Combine all the solutions

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

Merge Overlapping Intervals

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

sin (2 x) = 2

sin (2 x) = sin (4 x)

2 tan^{3} (x) - \frac{2}{3} tan (x) = 0

sin (2 x) = sin (3 x)

8 sin (θ) - 1 = 6 sin (θ)

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