Prove the Product-to-Sum Identity sin A cos B = (1/2)[sin(A+B)+sin(A-B)] Start with the right-hand side: (1/2)[sin(A+B)+sin(A-B)] = = (1/2)[(sinA)( =(1/2)[2( =sin A)( cos A)( B)+( B)] = B) +0] A)( B) + (sinA)( B)-(
Prove the Product-to-Sum Identity sin A cos B = (1/2)[sin(A+B)+sin(A-B)] Start with the right-hand side: (1/2)[sin(A+B)+sin(A-B)] = = (1/2)[(sinA)( =(1/2)[2( =sin A)( cos A)( B)+( B)] = B) +0] A)( B) + (sinA)( B)-(
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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![Prove the Product-to-Sum Identity
sin A cos B = (1/2)[sin(A+B)+sin(A-B)]
Start with the right-hand side:
(1/2) [sin(A+B)+sin(A-B)]
=
= (1/2)[(sinA)(
=(1/2)[2(
=sin
A)(
COS
A)(
The last expression is the
complete.
B) + (
B)] =
B) +0]
A)(
B) + (sinA)(
B)-(
-hand side of the original equation, hence, the proof is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1a1f503-504e-4e54-b1b4-a9349f6634ba%2F77c49fb4-7a22-42fe-b958-5a659ab7a645%2Fjuwao4l_processed.png&w=3840&q=75)
Transcribed Image Text:Prove the Product-to-Sum Identity
sin A cos B = (1/2)[sin(A+B)+sin(A-B)]
Start with the right-hand side:
(1/2) [sin(A+B)+sin(A-B)]
=
= (1/2)[(sinA)(
=(1/2)[2(
=sin
A)(
COS
A)(
The last expression is the
complete.
B) + (
B)] =
B) +0]
A)(
B) + (sinA)(
B)-(
-hand side of the original equation, hence, the proof is
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