Problem 1
Question
Fill in the blank to complete the trigonometric identity. $$\frac{1}{\tan u}=\text{_____}$$
Step-by-Step Solution
Verified Answer
\(\cot(u)\
1Step 1: Conversion
Convert \(\tan(u)\) to \(\frac{\sin(u)}{\cos(u)}\), thereby re-writing the problem: \(\frac{1}{\tan u} = \frac{1}{\frac{\sin(u)}{\cos(u)}}\)
2Step 2: Simplification
Simplify the problem using the property that the reciprocal of a fraction is the fraction with numerator and denominator switched: \(\frac{1}{\frac{\sin(u)}{\cos(u)}} = \frac{\cos(u)}{\sin(u)}\)
3Step 3: Identify the trigonometric identity
\(\frac{\cos(u)}{\sin(u)}\) is the definition of \(\cot(u)\). Therefore \(\frac{1}{\tan u} = \cot(u)\).
Other exercises in this chapter
Problem 1
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