Chapter 8, Problem 8RE

To determine

To find: The exact value of the given expression.

Answer to Problem 8RE

The exact value is 1.

Explanation of Solution

Given:

The expression is $\frac{\tan 40°}{\cot 50°}$ .

Calculation:

Solve the given expression using trigonometric identities to determine the exact value.

  $\begin{array}{c}\frac{\tan 40°}{\cot 50°}=\frac{\cot \left(90°-40°\right)}{\cot 50°}\left[\because \tan \theta =\cot \left(90°-\theta \right)\right]\\ =\frac{\cot 50°}{\cot 50°}\\ =1\end{array}$

So, the exact value is 1.