2. Apply the law of cosines to the triangle in the figure below to derive the compound angle formula for cos(A – B). P A B 1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 24E
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Question
1.
A proof of the triangle inequality: Justify each of the numbered steps in the
following proof of the triangle inequality.
|a + b|2 = (a + b)²
V.
(1)
= a? + 2ab + b²
A TRIANGLE
EQUALITY
know
your
nght
NOW!
< a² + 2|a||b| + b²
= |a|2 + 2|a||b| + |b|?
(|a| + |b|)?
(2)
(3)
|a + b| < |a| + |b|
(4)
2007
O COURTNEY GIBBONS
2.
Apply the law of cosines to the triangle in the figure below to derive the compound
angle formula for cos(A – B).
y
1
P
A
В
1
1
Transcribed Image Text:1. A proof of the triangle inequality: Justify each of the numbered steps in the following proof of the triangle inequality. |a + b|2 = (a + b)² V. (1) = a? + 2ab + b² A TRIANGLE EQUALITY know your nght NOW! < a² + 2|a||b| + b² = |a|2 + 2|a||b| + |b|? (|a| + |b|)? (2) (3) |a + b| < |a| + |b| (4) 2007 O COURTNEY GIBBONS 2. Apply the law of cosines to the triangle in the figure below to derive the compound angle formula for cos(A – B). y 1 P A В 1 1
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