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

The general solution for 3cos(x)+sin(x)=cos(x)-2sin(x) is x=-0.58800…+pin

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

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

x = - 0.58800 \dots + πn

Solution steps

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

Subtract

cos (x) - 2 sin (x)

from both sides

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

Rewrite using trig identities

2 + 3 tan (x) = 0

Move

2

to the right side

3 tan (x) = - 2

Divide both sides by

3

tan (x) = - \frac{2}{3}

Apply trig inverse properties

x = arctan (- \frac{2}{3}) + πn

Show solutions in decimal form

x = - 0.58800 \dots + πn

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

tan^{2} (x) - sin (x) = tan^{2} (x) sin^{2} (x)

3 cos (a) - 1 = 0

tan^{2} (x) + tan (x) + cot (x) + cot^{2} (x) = 4

tan (a) = 0

What is the general solution for 3cos(x)+sin(x)=cos(x)-2sin(x) ?
The general solution for 3cos(x)+sin(x)=cos(x)-2sin(x) is x=-0.58800…+pin