What is the general solution for 1/(tan(x))=0.5 ?

The general solution for 1/(tan(x))=0.5 is x=1.10714…+pin

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1/(tan(x))=0.5

\frac{1}{tan ( x )} = 0.5

x = 1.10714 \dots + πn

Degrees

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

\frac{1}{tan ( x )} = 0.5

Multiply both sides by

tan (x)

\frac{1}{tan ( x )} = 0.5

Multiply both sides by

tan (x)

\frac{1}{tan ( x )} tan (x) = 0.5 tan (x)

Simplify

1 = 0.5 tan (x)

1 = 0.5 tan (x)

Switch sides

0.5 tan (x) = 1

Divide both sides by

0.5

0.5 tan (x) = 1

Divide both sides by

0.5

\frac{0.5 tan ( x )}{0.5} = \frac{1}{0.5}

Simplify

tan (x) = 2

tan (x) = 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) = 2

Apply trig inverse properties

tan (x) = 2

General solutions for

tan (x) = 2

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

x = arctan (2) + πn

x = arctan (2) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn

tan (θ) = - \frac{16.54}{34.01}

sin (\frac{x}{7}) = \frac{3 ^{\frac{1}{2}}}{2}, π < x < 3 π

2 sec^{2} (x) - 13 sec (x) + 20 = 0, 2 π \leq x \leq 4 π

1 = - sin (x)

cos (4 5^{\circ} - x) = \frac{1}{2}

What is the general solution for 1/(tan(x))=0.5 ?
The general solution for 1/(tan(x))=0.5 is x=1.10714…+pin