What is the general solution for 1/(tan(x))=2 ?

The general solution for 1/(tan(x))=2 is x=0.46364…+pin

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1/(tan(x))=2

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

x = 0.46364 \dots + πn

Degrees

x = 26.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Multiply both sides by

tan (x)

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

Multiply both sides by

tan (x)

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

Simplify

1 = 2 tan (x)

1 = 2 tan (x)

Switch sides

2 tan (x) = 1

Divide both sides by

2

2 tan (x) = 1

Divide both sides by

2

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

Simplify

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

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

Verify Solutions

Find undefined (singularity) points:

tan (x) = 0

Take the denominator(s) of

\frac{1}{tan ( x )}

and compare to zero

tan (x) = 0

The following points are undefined

tan (x) = 0

Combine undefined points with solutions:

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (\frac{1}{2}) + πn

x = arctan (\frac{1}{2}) + πn

Show solutions in decimal form

x = 0.46364 \dots + πn

sin (\frac{π x}{10}) = 0

sec^{2} (x) cot (x) = 8

2 cos^{2} (y) - sin (y) - 1 = 0

sin (θ) = 0.61927

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

What is the general solution for 1/(tan(x))=2 ?
The general solution for 1/(tan(x))=2 is x=0.46364…+pin