Prove the identity. sin (x-y) cosx cosy tan.x - tany Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed de the right of the Rule. Statomont Pulo

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Prove the identity.
cos (x-y) sinx-sin (x-y) cosx = siny
OO EXPLANATION
We'll start with the left side.
We'll transform it step by step until it is identical to the right side.
cos (x−y) sinx-sin(x−y) cosx
=(cosx cosy+ sinx siny) sinx
−(sinx cosy− cosx siny) cosx
=sinx cosx cosy+sin’x siny
− sinx cosx cosy+cos‘x siny
sin²x siny+ cos²x siny
= siny (sin²x + cos²x)
= siny
Here is one possible answer.
EANSWER
=
=
Statement
More
sin²x siny + cos²x siny
Sum and difference identities:
cos (u-v) = cos u cos v + sinu sinv
sin (u-v) = sinu cos v- cosu sin v
siny (sin²x + cos²x)
Algebra
cos (x - y) sinx - sin(x - y) cosx
= siny
Algebra
Algebra
(cosx cosy + sinx siny) sinx − (sinx cosy – cosx siny) cosx
Pythagorean identity:
sin²u+ cos²u = 1
sinx cosx cosy + sin’x siny - sinx cosx cosy + cos’x siny
Rule
Sum and Difference
Algebra
Algebra
Algebra
Pythagorean
Transcribed Image Text:Prove the identity. cos (x-y) sinx-sin (x-y) cosx = siny OO EXPLANATION We'll start with the left side. We'll transform it step by step until it is identical to the right side. cos (x−y) sinx-sin(x−y) cosx =(cosx cosy+ sinx siny) sinx −(sinx cosy− cosx siny) cosx =sinx cosx cosy+sin’x siny − sinx cosx cosy+cos‘x siny sin²x siny+ cos²x siny = siny (sin²x + cos²x) = siny Here is one possible answer. EANSWER = = Statement More sin²x siny + cos²x siny Sum and difference identities: cos (u-v) = cos u cos v + sinu sinv sin (u-v) = sinu cos v- cosu sin v siny (sin²x + cos²x) Algebra cos (x - y) sinx - sin(x - y) cosx = siny Algebra Algebra (cosx cosy + sinx siny) sinx − (sinx cosy – cosx siny) cosx Pythagorean identity: sin²u+ cos²u = 1 sinx cosx cosy + sin’x siny - sinx cosx cosy + cos’x siny Rule Sum and Difference Algebra Algebra Algebra Pythagorean
Prove the identity.
sin (x-y)
cosx cosy
Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button to
the right of the Rule.
Statement
= tanx-tany
sin (x - y)
COS. COSy
0
Validate
Rule
Select Rule
ロ・ロ
cos
cot
J
Xx
00
sin
☐sec
tan
csc
0/6
Transcribed Image Text:Prove the identity. sin (x-y) cosx cosy Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button to the right of the Rule. Statement = tanx-tany sin (x - y) COS. COSy 0 Validate Rule Select Rule ロ・ロ cos cot J Xx 00 sin ☐sec tan csc 0/6
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