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

The general solution for 3(sin(x)-cos(x))=2(sin(x)+cos(x)) is x=1.37340…+pin

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

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

x = 1.37340 \dots + πn

Degrees

x = 78.69006 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Subtract

2 (sin (x) + cos (x))

from both sides

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

Rewrite using trig identities

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

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

tan (x) - 5 = 0

tan (x) - 5 = 0

Move

5

to the right side

tan (x) - 5 = 0

Add

5

to both sides

tan (x) - 5 + 5 = 0 + 5

Simplify

tan (x) = 5

tan (x) = 5

Apply trig inverse properties

tan (x) = 5

General solutions for

tan (x) = 5

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

x = arctan (5) + πn

x = arctan (5) + πn

Show solutions in decimal form

x = 1.37340 \dots + πn

What is the general solution for 3(sin(x)-cos(x))=2(sin(x)+cos(x)) ?
The general solution for 3(sin(x)-cos(x))=2(sin(x)+cos(x)) is x=1.37340…+pin