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

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

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9cos(2θ)=-9cos(θ)

9 cos (2 θ) = - 9 cos (θ)

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

Solution steps

9 cos (2 θ) = - 9 cos (θ)

Subtract

- 9 cos (θ)

from both sides

9 cos (2 θ) + 9 cos (θ) = 0

Rewrite using trig identities

(- 1 + 2 cos^{2} (θ)) \cdot 9 + 9 cos (θ) = 0

Solve by substitution

cos (θ) = \frac{1}{2}, cos (θ) = - 1

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

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

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

3 sec^{2} (x) - 3 sec (x) = 6

tan (2 θ) = - 3

sin (x) + cos (x) = \frac{2}{5}

2 cos (x) + 2 sin (x) cos (x) = 0

100 cos (3 0^{\circ}) - 200 cos (θ) = 0

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