What is the general solution for 7cos^2(θ)-3=-2cos(θ)+2 ?

The general solution for 7cos^2(θ)-3=-2cos(θ)+2 is θ=0.77519…+2pin,θ=2pi-0.77519…+2pin,θ=pi+2pin

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7cos^2(θ)-3=-2cos(θ)+2

7 cos^{2} (θ) - 3 = - 2 cos (θ) + 2

θ = 0.77519 \dots + 2 πn, θ = 2 π - 0.77519 \dots + 2 πn, θ = π + 2 πn

Solution steps

7 cos^{2} (θ) - 3 = - 2 cos (θ) + 2

Solve by substitution

cos (θ) = \frac{5}{7}, cos (θ) = - 1

cos (θ) = \frac{5}{7} : θ = arccos (\frac{5}{7}) + 2 πn, θ = 2 π - arccos (\frac{5}{7}) + 2 πn

cos (θ) = - 1 : θ = π + 2 πn

Combine all the solutions

θ = arccos (\frac{5}{7}) + 2 πn, θ = 2 π - arccos (\frac{5}{7}) + 2 πn, θ = π + 2 πn

Show solutions in decimal form

θ = 0.77519 \dots + 2 πn, θ = 2 π - 0.77519 \dots + 2 πn, θ = π + 2 πn

\frac{sin ( 2 x )}{2} = sin (x)

sin^{2} (θ) + sin (θ) - 6 = 0

y, x + tan (x y) = 0

- sin (2 θ) = 0

∣ cos (2 x) ∣ = 1

What is the general solution for 7cos^2(θ)-3=-2cos(θ)+2 ?
The general solution for 7cos^2(θ)-3=-2cos(θ)+2 is θ=0.77519…+2pin,θ=2pi-0.77519…+2pin,θ=pi+2pin