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

The general solution for 3(2sin(x)-cos(x))=2(sin(x)-3cos(x)) is x=-0.64350…+pin

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

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

x = - 0.64350 \dots + πn

Degrees

x = - 36.86989 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Subtract

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

from both sides

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

Rewrite using trig identities

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

Divide both sides by

cos (x), cos (x) \neq = 0

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

Simplify

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

4 tan (x) + 3 = 0

4 tan (x) + 3 = 0

Move

3

to the right side

4 tan (x) + 3 = 0

Subtract

3

from both sides

4 tan (x) + 3 - 3 = 0 - 3

Simplify

4 tan (x) = - 3

4 tan (x) = - 3

Divide both sides by

4

4 tan (x) = - 3

Divide both sides by

4

\frac{4 tan ( x )}{4} = \frac{- 3}{4}

Simplify

tan (x) = - \frac{3}{4}

tan (x) = - \frac{3}{4}

Apply trig inverse properties

tan (x) = - \frac{3}{4}

General solutions for

tan (x) = - \frac{3}{4}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{3}{4}) + πn

x = arctan (- \frac{3}{4}) + πn

Show solutions in decimal form

x = - 0.64350 \dots + πn

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

tan (θ) = \frac{7}{6}

2 sin (x) + 5 = 6

sin (2 θ) - cos (2 θ) = 1

cos (θ) = \frac{1}{3}

What is the general solution for 3(2sin(x)-cos(x))=2(sin(x)-3cos(x)) ?
The general solution for 3(2sin(x)-cos(x))=2(sin(x)-3cos(x)) is x=-0.64350…+pin