What is the general solution for 3cos(2θ)=9cos(θ)-6 ?

The general solution for 3cos(2θ)=9cos(θ)-6 is θ=2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin

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3cos(2θ)=9cos(θ)-6

3 cos (2 θ) = 9 cos (θ) - 6

θ = 2 πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Solution steps

3 cos (2 θ) = 9 cos (θ) - 6

Subtract

9 cos (θ) - 6

from both sides

3 cos (2 θ) - 9 cos (θ) + 6 = 0

Rewrite using trig identities

3 + 6 cos^{2} (θ) - 9 cos (θ) = 0

Solve by substitution

cos (θ) = 1, cos (θ) = \frac{1}{2}

cos (θ) = 1 : θ = 2 πn

cos (θ) = \frac{1}{2} : θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

Combine all the solutions

θ = 2 πn, θ = \frac{π}{3} + 2 πn, θ = \frac{5 π}{3} + 2 πn

4 sin (\frac{x}{3}) - 3 = 0

0 = sin (c)

sin (θ) = - \frac{5}{13}, sec (θ)

3 cosh (x) + 5 sinh (x) = - 3

sin (a) = 2 (1 - cos (a))

What is the general solution for 3cos(2θ)=9cos(θ)-6 ?
The general solution for 3cos(2θ)=9cos(θ)-6 is θ=2pin,θ= pi/3+2pin,θ=(5pi)/3+2pin