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
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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DUE NOW. Please answer the question as the same on the process on what's in the example and put all the answers in the tables identified its rule. Please write the answer on paper, not type. Thank you!
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff74350d9-c03f-47a9-a1da-c39263a3a70f%2F453a1304-7cea-496c-844c-fb8ba8693165%2Fyb4meff_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff74350d9-c03f-47a9-a1da-c39263a3a70f%2F453a1304-7cea-496c-844c-fb8ba8693165%2Fhdb0hv4_processed.png&w=3840&q=75)
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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