What is the general solution for 2cos(θ)=2cos(3θ) ?

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

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2cos(θ)=2cos(3θ)

2 cos (θ) = 2 cos (3 θ)

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

Solution steps

2 cos (θ) = 2 cos (3 θ)

Subtract

2 cos (3 θ)

from both sides

2 cos (θ) - 2 cos (3 θ) = 0

Rewrite using trig identities

8 cos (θ) - 8 cos^{3} (θ) = 0

Solve by substitution

cos (θ) = 0, cos (θ) = - 1, cos (θ) = 1

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

cos (θ) = - 1 : θ = π + 2 πn

cos (θ) = 1 : θ = 2 πn

Combine all the solutions

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

cos (t) + cos (2 t) = - 0.75

9.8 \cdot sin (α) - 1.96 \cdot cos (α) = 0.47

1 = \frac{2 - sin ( x )}{sin ^{2} ( x )}

2 - 5 cos (x + 1) = 4

2 (tan (θ) + 3) = 5 + tan (θ)

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