What is the general solution for 2cos^2(θ)-sin(θ)=2 ?

The general solution for 2cos^2(θ)-sin(θ)=2 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin,θ=2pin,θ=pi+2pin

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2cos^2(θ)-sin(θ)=2

2 cos^{2} (θ) - sin (θ) = 2

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = 2 πn, θ = π + 2 πn

Solution steps

2 cos^{2} (θ) - sin (θ) = 2

Subtract

2

from both sides

2 cos^{2} (θ) - sin (θ) - 2 = 0

Rewrite using trig identities

- sin (θ) - 2 sin^{2} (θ) = 0

Solve by substitution

sin (θ) = - \frac{1}{2}, sin (θ) = 0

sin (θ) = - \frac{1}{2} : θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn

sin (θ) = 0 : θ = 2 πn, θ = π + 2 πn

Combine all the solutions

θ = \frac{7 π}{6} + 2 πn, θ = \frac{11 π}{6} + 2 πn, θ = 2 πn, θ = π + 2 πn

θ, 2 sin^{2} (θ) = 1 - sin (θ)

cos (a) = \frac{57}{113 \cdot 78}

tan^{2} (x) + tan (x) - 12 = 2

x, cos^{2} (x + x y) = \frac{3}{2}

sin (o) = \frac{3}{5}

What is the general solution for 2cos^2(θ)-sin(θ)=2 ?
The general solution for 2cos^2(θ)-sin(θ)=2 is θ=(7pi)/6+2pin,θ=(11pi)/6+2pin,θ=2pin,θ=pi+2pin