What is the general solution for (cos(x)-3sin(x))/(sin(x)+3cos(x))=-1/2 ?

The general solution for (cos(x)-3sin(x))/(sin(x)+3cos(x))=-1/2 is x= pi/4+pin

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(cos(x)-3sin(x))/(sin(x)+3cos(x))=-1/2

\frac{cos ( x ) - 3 sin ( x )}{sin ( x ) + 3 cos ( x )} = - \frac{1}{2}

x = \frac{π}{4} + πn

Solution steps

\frac{cos ( x ) - 3 sin ( x )}{sin ( x ) + 3 cos ( x )} = - \frac{1}{2}

Subtract

- \frac{1}{2}

from both sides

\frac{cos ( x ) - 3 sin ( x )}{sin ( x ) + 3 cos ( x )} + \frac{1}{2} = 0

Simplify

\frac{cos ( x ) - 3 sin ( x )}{sin ( x ) + 3 cos ( x )} + \frac{1}{2} : \frac{5 cos ( x ) - 5 sin ( x )}{2 ( sin ( x ) + 3 cos ( x ) )}

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

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

5 cos (x) - 5 sin (x) = 0

Rewrite using trig identities

5 - 5 tan (x) = 0

Move

5

to the right side

- 5 tan (x) = - 5

Divide both sides by

- 5

tan (x) = 1

General solutions for

tan (x) = 1

x = \frac{π}{4} + πn

cos (\frac{π}{2} - x) = 0

1 sin (4 5^{\circ}) = 2.42 sin (r)

sec (x) = 4 sin (x)

sinh (nπ) = 0

x, z = sin (x y^{2})

What is the general solution for (cos(x)-3sin(x))/(sin(x)+3cos(x))=-1/2 ?
The general solution for (cos(x)-3sin(x))/(sin(x)+3cos(x))=-1/2 is x= pi/4+pin