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

The general solution for sin^2(x)-3sin(x)cos(x)+2cos^2(x)=0 is x= pi/4+pin,x=1.10714…+pin

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

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

x = \frac{π}{4} + πn, x = 1.10714 \dots + πn

Solution steps

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

Factor

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

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

Solving each part separately

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

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

sin (x) - 2 cos (x) = 0 : x = arctan (2) + πn

Combine all the solutions

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

Show solutions in decimal form

x = \frac{π}{4} + πn, x = 1.10714 \dots + πn

2 csc^{2} (x) - 2 csc (x) - 2 = 0

sin (t) = - \frac{2}{2}

9 cos (2 θ) = 9 cos^{2} (θ) - 4

- 10 sin (x) = 0

sin (\frac{x}{5}) = 0

What is the general solution for sin^2(x)-3sin(x)cos(x)+2cos^2(x)=0 ?
The general solution for sin^2(x)-3sin(x)cos(x)+2cos^2(x)=0 is x= pi/4+pin,x=1.10714…+pin