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Chapter 6: Problem 1

Fill in the blank to complete the trigonometric identity. $$\frac{1}{\tan u}=\text{_____}$$

Short Answer

Expert verified
\(\cot(u)\

Step by step solution

01

Conversion

Convert \(\tan(u)\) to \(\frac{\sin(u)}{\cos(u)}\), thereby re-writing the problem: \(\frac{1}{\tan u} = \frac{1}{\frac{\sin(u)}{\cos(u)}}\)
02

Simplification

Simplify the problem using the property that the reciprocal of a fraction is the fraction with numerator and denominator switched: \(\frac{1}{\frac{\sin(u)}{\cos(u)}} = \frac{\cos(u)}{\sin(u)}\)
03

Identify the trigonometric identity

\(\frac{\cos(u)}{\sin(u)}\) is the definition of \(\cot(u)\). Therefore \(\frac{1}{\tan u} = \cot(u)\).

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