What is the general solution for 2sin^2(θ)-3sin(θ)cos(θ)+cos^2(θ)=0 ?

The general solution for 2sin^2(θ)-3sin(θ)cos(θ)+cos^2(θ)=0 is θ=0.46364…+pin,θ= pi/4+pin

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2sin^2(θ)-3sin(θ)cos(θ)+cos^2(θ)=0

2 sin^{2} (θ) - 3 sin (θ) cos (θ) + cos^{2} (θ) = 0

θ = 0.46364 \dots + πn, θ = \frac{π}{4} + πn

Solution steps

2 sin^{2} (θ) - 3 sin (θ) cos (θ) + cos^{2} (θ) = 0

Factor

2 sin^{2} (θ) - 3 sin (θ) cos (θ) + cos^{2} (θ) : (2 sin (θ) - cos (θ)) (sin (θ) - cos (θ))

(2 sin (θ) - cos (θ)) (sin (θ) - cos (θ)) = 0

Solving each part separately

2 sin (θ) - cos (θ) = 0 or sin (θ) - cos (θ) = 0

2 sin (θ) - cos (θ) = 0 : θ = arctan (\frac{1}{2}) + πn

sin (θ) - cos (θ) = 0 : θ = \frac{π}{4} + πn

Combine all the solutions

θ = arctan (\frac{1}{2}) + πn, θ = \frac{π}{4} + πn

Show solutions in decimal form

θ = 0.46364 \dots + πn, θ = \frac{π}{4} + πn

sin^{2} (x) + 4 cos^{2} (x) = 1

4 cos (x^{2}) - 3 = 0

sin (x) + 1 = 0, 0 \leq x < 2 π

θ, sin^{2} (θ) = \frac{1}{4}

cot (θ) = 3, 0 \leq θ < 2 π

What is the general solution for 2sin^2(θ)-3sin(θ)cos(θ)+cos^2(θ)=0 ?
The general solution for 2sin^2(θ)-3sin(θ)cos(θ)+cos^2(θ)=0 is θ=0.46364…+pin,θ= pi/4+pin