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

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

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2sin^2(x)-3sin(x)cos(x)+cos^2(x)=0

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

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

Solution steps

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

Factor

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

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

Solving each part separately

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

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

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

Combine all the solutions

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

Show solutions in decimal form

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

3 cos^{2} (x) = sin (x)

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

cos (4 + x) = 0.45

(tan (θ) - 2) (16 sin^{2} (θ) - 1) = 0

csc (θ) = 1.9

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