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

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

tan (x) - 5 = 0

Move

5

to the right side

tan (x) = 5

Apply trig inverse properties

x = arctan (5) + πn

Show solutions in decimal form

x = 1.37340 \dots + πn

\frac{sin ( 2 x )}{sin ( x )} = 1

θ, ma = t sin (θ) - m g

x, sin (x) - cos (y) - 2 = 0

\frac{cot ( a )}{cos ( a )} = cos (a)

cos (x) - 2 = 0

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