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

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

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

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

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

Solution steps

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

Factor

sin^{2} (x) - 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

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

\frac{cos ^{2} ( x ) + 1}{1 + cot ^{2} ( x )} = 1

3 sin^{2} (c) - 7 sin (x) + 2 = 0

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

cos (t) = cos (2 t)

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