What is the general solution for cos(3θ)=4cos(3θ)-3cos(θ) ?

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

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cos(3θ)=4cos(3θ)-3cos(θ)

cos (3 θ) = 4 cos (3 θ) - 3 cos (θ)

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

Solution steps

cos (3 θ) = 4 cos (3 θ) - 3 cos (θ)

Subtract

4 cos (3 θ) - 3 cos (θ)

from both sides

- 3 cos (3 θ) + 3 cos (θ) = 0

Rewrite using trig identities

12 cos (θ) - 12 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

sin^{2} (x) - 7 sin (x) = 0

sin (x) = \frac{48 sin ( 6 9 ^{\circ} )}{47.5}

2 cos^{2} (3 x) + cos (3 x) - 1 = 0

sin (3 x) = \frac{- 3}{4}

4 cos (x - 4 5^{\circ}) + 7 = 10

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