What is the general solution for 2/(tan(x))=3-tan(x) ?

The general solution for 2/(tan(x))=3-tan(x) is x= pi/4+pin,x=1.10714…+pin

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2/(tan(x))=3-tan(x)

\frac{2}{tan ( x )} = 3 - tan (x)

x = \frac{π}{4} + πn, x = 1.10714 \dots + πn

Solution steps

\frac{2}{tan ( x )} = 3 - tan (x)

Solve by substitution

tan (x) = 1, tan (x) = 2

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = 2 : x = arctan (2) + πn

Combine all the solutions

x = \frac{π}{4} + πn, x = arctan (2) + πn

Show solutions in decimal form

x = \frac{π}{4} + πn, x = 1.10714 \dots + πn

tan (x) = 0.158

- 1 = sin (4.18879 x)

\frac{1}{sin ( x ) cos ( x )} = 22

tan (x) = \frac{1}{5 ^{\frac{1}{2}}}

3 csc (\frac{x}{2}) - 2 = 0

What is the general solution for 2/(tan(x))=3-tan(x) ?
The general solution for 2/(tan(x))=3-tan(x) is x= pi/4+pin,x=1.10714…+pin