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

The general solution for 3cos(2θ)=-9cos(θ)-6 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=pi+2pin

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3cos(2θ)=-9cos(θ)-6

3 cos (2 θ) = - 9 cos (θ) - 6

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = π + 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) = - \frac{1}{2}, cos (θ) = - 1

cos (θ) = - \frac{1}{2} : θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = \frac{2 π}{3} + 2 πn, θ = \frac{4 π}{3} + 2 πn, θ = π + 2 πn

5 sin (x) cos (x) + cos (x) = 0

1 + cos (θ) = 2 sin^{2} (θ)

cos (2 a) = - \frac{4}{7}

cos (\frac{π}{60}) - cos (\frac{π}{60}) = sin (x)

3 tan^{2} (α) - 3 tan (α) = 0

What is the general solution for 3cos(2θ)=-9cos(θ)-6 ?
The general solution for 3cos(2θ)=-9cos(θ)-6 is θ=(2pi)/3+2pin,θ=(4pi)/3+2pin,θ=pi+2pin