Answered: How do we arrive at a formula for the…

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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How do we arrive at a formula for the product sin A cos B?

Expert Solution

Step 1

We have to derive an expression for $\sin (A) \cos (B)$ .

We start off with the sum of angles formulae $\{\begin{cases} \sin (A + B) = \sin A \cos B + \cos A \sin B \\ \sin (A - B) = \sin A \cos B - \cos A \sin B \end{cases}$

Adding these expressions vertically, we obtain: $\sin (A + B) + \sin (A - B) = 2 \sin A \cos B$ .

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$Half-angle, Double-angle, and Product-Sum Formulae$

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