What is the general solution for 7cos^2(θ)+6cos(θ)-12=7cos(θ)-6 ?

The general solution for 7cos^2(θ)+6cos(θ)-12=7cos(θ)-6 is θ=2pin,θ=2.60049…+2pin,θ=-2.60049…+2pin

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7cos^2(θ)+6cos(θ)-12=7cos(θ)-6

7 cos^{2} (θ) + 6 cos (θ) - 12 = 7 cos (θ) - 6

θ = 2 πn, θ = 2.60049 \dots + 2 πn, θ = - 2.60049 \dots + 2 πn

Solution steps

7 cos^{2} (θ) + 6 cos (θ) - 12 = 7 cos (θ) - 6

Solve by substitution

cos (θ) = 1, cos (θ) = - \frac{6}{7}

cos (θ) = 1 : θ = 2 πn

cos (θ) = - \frac{6}{7} : θ = arccos (- \frac{6}{7}) + 2 πn, θ = - arccos (- \frac{6}{7}) + 2 πn

Combine all the solutions

θ = 2 πn, θ = arccos (- \frac{6}{7}) + 2 πn, θ = - arccos (- \frac{6}{7}) + 2 πn

Show solutions in decimal form

θ = 2 πn, θ = 2.60049 \dots + 2 πn, θ = - 2.60049 \dots + 2 πn

sin^{2} (x) = sin (x) + 1 - sin^{2} (x)

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

cos (5 t) cos (2 t) = - sin (5 t) sin (2 t)

x, cos (x) = sin (y)

tan (θ) = \frac{5}{8}

What is the general solution for 7cos^2(θ)+6cos(θ)-12=7cos(θ)-6 ?
The general solution for 7cos^2(θ)+6cos(θ)-12=7cos(θ)-6 is θ=2pin,θ=2.60049…+2pin,θ=-2.60049…+2pin