What is the general solution for -3cos^2(θ)-10cos(θ)=-3cos(θ)-6 ?

The general solution for -3cos^2(θ)-10cos(θ)=-3cos(θ)-6 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin

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-3cos^2(θ)-10cos(θ)=-3cos(θ)-6

- 3 cos^{2} (θ) - 10 cos (θ) = - 3 cos (θ) - 6

θ = 0.84106 \dots + 2 πn, θ = 2 π - 0.84106 \dots + 2 πn

Solution steps

- 3 cos^{2} (θ) - 10 cos (θ) = - 3 cos (θ) - 6

Solve by substitution

cos (θ) = - 3, cos (θ) = \frac{2}{3}

cos (θ) = - 3 :

No Solution

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

Combine all the solutions

θ = arccos (\frac{2}{3}) + 2 πn, θ = 2 π - arccos (\frac{2}{3}) + 2 πn

Show solutions in decimal form

θ = 0.84106 \dots + 2 πn, θ = 2 π - 0.84106 \dots + 2 πn

- 4 sin (x) = - cos^{2} (x) + 4

sin^{2} (x) - 4 sin (x) + 3 = 0

6 sin (x) + csc (x) = 0

cot^{2} (x) - 3 csc (x) = - 3

tan (4 x) = 0

What is the general solution for -3cos^2(θ)-10cos(θ)=-3cos(θ)-6 ?
The general solution for -3cos^2(θ)-10cos(θ)=-3cos(θ)-6 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin