What is the general solution for (3sin(x)-cos(x))/(sin(x)+cos(x))=4 ?

The general solution for (3sin(x)-cos(x))/(sin(x)+cos(x))=4 is x=-1.37340…+pin

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(3sin(x)-cos(x))/(sin(x)+cos(x))=4

\frac{3 sin ( x ) - cos ( x )}{sin ( x ) + cos ( x )} = 4

x = - 1.37340 \dots + πn

Solution steps

\frac{3 sin ( x ) - cos ( x )}{sin ( x ) + cos ( x )} = 4

Subtract

4

from both sides

\frac{3 sin ( x ) - cos ( x )}{sin ( x ) + cos ( x )} - 4 = 0

Simplify

\frac{3 sin ( x ) - cos ( x )}{sin ( x ) + cos ( x )} - 4 : \frac{- sin ( x ) - 5 cos ( x )}{sin ( x ) + cos ( x )}

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

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

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

Rewrite using trig identities

- tan (x) - 5 = 0

Move

5

to the right side

- tan (x) = 5

Divide both sides by

- 1

tan (x) = - 5

Apply trig inverse properties

x = arctan (- 5) + πn

Show solutions in decimal form

x = - 1.37340 \dots + πn

\frac{1}{e ^{s i n (x)}} = 1

∣ cos (x) ∣ = \frac{3}{2}

tan (θ) = \frac{- 1}{3}, 0^{\circ} \leq θ \leq 36 0^{\circ}

4 cos (\frac{π}{4} (x + 3)) = 0

sin^{3} (x) = cos (x)

What is the general solution for (3sin(x)-cos(x))/(sin(x)+cos(x))=4 ?
The general solution for (3sin(x)-cos(x))/(sin(x)+cos(x))=4 is x=-1.37340…+pin