What is the general solution for cos(θ)cos(3θ)-1=0 ?

The general solution for cos(θ)cos(3θ)-1=0 is θ=2pin,θ=pi+2pin

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cos(θ)cos(3θ)-1=0

cos (θ) cos (3 θ) - 1 = 0

θ = 2 πn, θ = π + 2 πn

Solution steps

cos (θ) cos (3 θ) - 1 = 0

Rewrite using trig identities

- 1 + (- 3 cos (θ) + 4 cos^{3} (θ)) cos (θ) = 0

Solve by substitution

cos (θ) = 1, cos (θ) = - 1, cos (θ) = i \frac{1}{2}, cos (θ) = - i \frac{1}{2}

cos (θ) = 1 : θ = 2 πn

cos (θ) = - 1 : θ = π + 2 πn

cos (θ) = i \frac{1}{2} :

No Solution

cos (θ) = - i \frac{1}{2} :

No Solution

Combine all the solutions

θ = 2 πn, θ = π + 2 πn

2 tan (θ) sin (θ) - tan (θ) = 0

sin (4 x + \frac{π}{4}) = 1

cos^{2} (x) - cos (x) = 0, (0, 2 π)

csc (4 2^{\circ}) = sec (x)

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

What is the general solution for cos(θ)cos(3θ)-1=0 ?
The general solution for cos(θ)cos(3θ)-1=0 is θ=2pin,θ=pi+2pin