Q. 12 - Precalculus Enhanced with Graphing Utilities

Question

Find the exact value of each expression. Do not use a calculator.

$sec{50}^{\circ }\cos {50}^{\circ }$

Step-by-Step Solution

Answer

The value of the given expression is 1.

Step 1. Given

Given trigonometric function

$sec{50}^{\circ }\cos {50}^{\circ }$

Step 2. Concept

We will use standard formula of  $\sin \theta$ and $\cos \theta$ at different angles for calculating the final result of given expression.

Step 3. Calculation

We know

$$\begin{gathered} sec\theta =\frac{1}{\cos \theta } \\ therefore \\ sec{50}^{\circ }=\frac{1}{\cos {50}^{\circ }} \\ Now substituting in the given expression we get, \\ sec{50}^{\circ }\cos {50}^{\circ } \\ =\frac{1}{\cos {50}^{\circ }}\cos {50}^{\circ } \\ =1 \end{gathered}$$