What is the general solution for 1/(tan(x))=4 ?

The general solution for 1/(tan(x))=4 is x=0.24497…+pin

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1/(tan(x))=4

\frac{1}{tan ( x )} = 4

x = 0.24497 \dots + πn

Degrees

x = 14.03624 \dots^{\circ} + 18 0^{\circ} n

Solution steps

\frac{1}{tan ( x )} = 4

Multiply both sides by

tan (x)

\frac{1}{tan ( x )} = 4

Multiply both sides by

tan (x)

\frac{1}{tan ( x )} tan (x) = 4 tan (x)

Simplify

1 = 4 tan (x)

1 = 4 tan (x)

Switch sides

4 tan (x) = 1

Divide both sides by

4

4 tan (x) = 1

Divide both sides by

4

\frac{4 tan ( x )}{4} = \frac{1}{4}

Simplify

tan (x) = \frac{1}{4}

tan (x) = \frac{1}{4}

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}{4}

Apply trig inverse properties

tan (x) = \frac{1}{4}

General solutions for

tan (x) = \frac{1}{4}

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

x = arctan (\frac{1}{4}) + πn

x = arctan (\frac{1}{4}) + πn

Show solutions in decimal form

x = 0.24497 \dots + πn

sin^{2} (x) + 2 - 3 sin (x) = cos^{2} (x)

4 sin^{2} (θ) - 4 cos (θ) = 1

\frac{33}{sin ( x )} = \frac{29}{sin ( 10 0 ^{\circ} )}

2 cos^{2} (x) - 1 = sin (x)

(\frac{1}{2}) = cos (θ)

What is the general solution for 1/(tan(x))=4 ?
The general solution for 1/(tan(x))=4 is x=0.24497…+pin