What is the general solution for -cos(θ)+1=2cos(θ)+3 ?

The general solution for -cos(θ)+1=2cos(θ)+3 is θ=2.30052…+2pin,θ=-2.30052…+2pin

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-cos(θ)+1=2cos(θ)+3

- cos (θ) + 1 = 2 cos (θ) + 3

θ = 2.30052 \dots + 2 πn, θ = - 2.30052 \dots + 2 πn

Solution steps

- cos (θ) + 1 = 2 cos (θ) + 3

Solve by substitution

cos (θ) = - \frac{2}{3}

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

Combine all the solutions

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

Show solutions in decimal form

θ = 2.30052 \dots + 2 πn, θ = - 2.30052 \dots + 2 πn

cot^{2} (x) + cot (x) = 0

3 cos (2 θ) + 9 cos (θ) - 4 = - 2 cos (θ)

16 cos^{2} (x) - 12 = 0

cos (2 θ) - cos^{2} (θ) = 0

3 tan^{2} (x) + 5 tan (x) - 4 = 0

What is the general solution for -cos(θ)+1=2cos(θ)+3 ?
The general solution for -cos(θ)+1=2cos(θ)+3 is θ=2.30052…+2pin,θ=-2.30052…+2pin