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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 2 (page 500)

Find the exact value of the expression:
$\cos 285 掳路 \cos 195 掳$

Short Answer

Expert verified

The exact value is $0$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$\cos 285 掳路 \cos 195 掳$

We know $\cos a 路 \cos b = \frac{1}{2} [\cos (a - b) + \cos (a + b)]$ .

Using the formula, we get,

$\cos 285 掳路 \cos 195 掳 = \frac{1}{2} [\cos (285 - 195) + \cos (285 + 195)]$

02

Step 2. Simplify the equation.

Continuing the above equation,

\cos 285 掳 路 \cos 195 掳 = \frac{1}{2} [\cos (120 掳) + \cos (480 掳)] \cos 285 掳 路 \cos 195 掳 = \frac{1}{2} [- \frac{1}{2} + (- \frac{1}{2})] \cos 285 掳 路 \cos 195 掳 = 0

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