What is the general solution for sin^2(x)-5sin(x)cos(x)+6cos^2(x)=0 ?

The general solution for sin^2(x)-5sin(x)cos(x)+6cos^2(x)=0 is x=1.10714…+pin,x=1.24904…+pin

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sin^2(x)-5sin(x)cos(x)+6cos^2(x)=0

sin^{2} (x) - 5 sin (x) cos (x) + 6 cos^{2} (x) = 0

x = 1.10714 \dots + πn, x = 1.24904 \dots + πn

Solution steps

sin^{2} (x) - 5 sin (x) cos (x) + 6 cos^{2} (x) = 0

Factor

sin^{2} (x) - 5 sin (x) cos (x) + 6 cos^{2} (x) : (sin (x) - 2 cos (x)) (sin (x) - 3 cos (x))

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

Solving each part separately

sin (x) - 2 cos (x) = 0 or sin (x) - 3 cos (x) = 0

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

sin (x) - 3 cos (x) = 0 : x = arctan (3) + πn

Combine all the solutions

x = arctan (2) + πn, x = arctan (3) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn, x = 1.24904 \dots + πn

cos (2 x) + 3 cos (x) = 2

6 sin (x) + 1 = 0

π + 3 arccos (x + 1) = 0

5 sin (2 x) + 3 cos (2 x) = 0

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

What is the general solution for sin^2(x)-5sin(x)cos(x)+6cos^2(x)=0 ?
The general solution for sin^2(x)-5sin(x)cos(x)+6cos^2(x)=0 is x=1.10714…+pin,x=1.24904…+pin