What is the general solution for 2cos(θ)-3=5cos(θ)-5 ?

The general solution for 2cos(θ)-3=5cos(θ)-5 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin

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2cos(θ)-3=5cos(θ)-5

2 cos (θ) - 3 = 5 cos (θ) - 5

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

Solution steps

2 cos (θ) - 3 = 5 cos (θ) - 5

Solve by substitution

cos (θ) = \frac{2}{3}

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

tan (θ) = \frac{4}{5}

tan^{2} (x) - sec (x) - 1 = 0

7 sin (x) cos (x) + 9 cos (x) = 0

2 cos (3 x) + 1 = 0

4 cos^{2} (x) - 3 = 0, 0 \leq x \leq 2 π

What is the general solution for 2cos(θ)-3=5cos(θ)-5 ?
The general solution for 2cos(θ)-3=5cos(θ)-5 is θ=0.84106…+2pin,θ=2pi-0.84106…+2pin