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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. 50 (page 504)

In Problems $45 - 52$ , find the exact value of each expression.
$\sin 70^{鈭�} \cos 40^{鈭�} - \cos 70^{鈭�} s i n 40^{鈭�}$ .

Short Answer

Expert verified

The exact value of the expression $\sin 70^{鈭�} \cos 40^{鈭�} - \cos 70^{鈭�} s i n 40^{鈭�}$ is, $\frac{1}{2}$ (or) $\sin (30^{鈭�})$ .

Step by step solution

01

Step 1 Given expression is,

$\sin 70^{鈭�} \cos 40^{鈭�} - \cos 70^{鈭�} s i n 40^{鈭�}$ .

The formula used in this problem is,

$\sin (A - B) = \sin A \cos B - \cos A \sin B$

02

Step 2 Apply the formula in the given expression.

$\sin 70^{鈭�} \cos 40^{鈭�} - \cos 70^{鈭�} s i n 40^{鈭�} = \sin (70^{鈭�} - 40^{鈭�}) = \sin (30^{鈭�})$

The value of $\sin (30^{鈭�})$ is, $\frac{1}{2}$ .

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