SlideShare a Scribd company logo
1 of 1
Download to read offline
Prove the hyperbolic function formula: sinhx(2x)=2sinhxcoshx
Solution
Just use the definitions of sinh(x) and cosh(x): sinh(x) = [e^x - e^(-x)]/2, cosh(x) =
[e^x + e^(-x)]/2 So, simply expand! sinh(2x) = [e^(2x) - e^(-2x)]/2 = [e^x - e^(-x)][e^x + e^(-
x)]/2 = 2 [[e^x - e^(-x)]/2][[e^x + e^(-x)]/2] = 2sinh(x)cosh(x)

More Related Content

More from arkurkuri

Use your thoughts about the essay, , and your own reflections on y.pdf
Use your thoughts about the essay, , and your own reflections on y.pdfUse your thoughts about the essay, , and your own reflections on y.pdf
Use your thoughts about the essay, , and your own reflections on y.pdf
arkurkuri
 
12-1 Group Work Preliminary and Program Development ResearchPurp.pdf
12-1 Group Work Preliminary and Program Development ResearchPurp.pdf12-1 Group Work Preliminary and Program Development ResearchPurp.pdf
12-1 Group Work Preliminary and Program Development ResearchPurp.pdf
arkurkuri
 
This homework consists of 8 problems. The first 7ask that .pdf
This homework consists of 8 problems. The first 7ask that .pdfThis homework consists of 8 problems. The first 7ask that .pdf
This homework consists of 8 problems. The first 7ask that .pdf
arkurkuri
 
The Hox genes are responsible for determining the anterior-posterior.pdf
The Hox genes are responsible for determining the anterior-posterior.pdfThe Hox genes are responsible for determining the anterior-posterior.pdf
The Hox genes are responsible for determining the anterior-posterior.pdf
arkurkuri
 
READ BEFORE YOU START You are given a partially completed pr.pdf
READ BEFORE YOU START  You are given a partially completed pr.pdfREAD BEFORE YOU START  You are given a partially completed pr.pdf
READ BEFORE YOU START You are given a partially completed pr.pdf
arkurkuri
 
Other diseases, called collagen vascular diseases, affect the protein.pdf
Other diseases, called collagen vascular diseases, affect the protein.pdfOther diseases, called collagen vascular diseases, affect the protein.pdf
Other diseases, called collagen vascular diseases, affect the protein.pdf
arkurkuri
 
Discuss the origins of mitochondria and chloroplasts. Look at them i.pdf
Discuss the origins of mitochondria and chloroplasts. Look at them i.pdfDiscuss the origins of mitochondria and chloroplasts. Look at them i.pdf
Discuss the origins of mitochondria and chloroplasts. Look at them i.pdf
arkurkuri
 
Match the following 1. Natural killer cells2. B cells3. Cy.pdf
Match the following 1. Natural killer cells2. B cells3. Cy.pdfMatch the following 1. Natural killer cells2. B cells3. Cy.pdf
Match the following 1. Natural killer cells2. B cells3. Cy.pdf
arkurkuri
 

More from arkurkuri (20)

2.51. Why does earth have seasons2. What is the origin of the t.pdf
2.51. Why does earth have seasons2. What is the origin of the t.pdf2.51. Why does earth have seasons2. What is the origin of the t.pdf
2.51. Why does earth have seasons2. What is the origin of the t.pdf
 
Write the product as a sum or difference. Write the product as a sum.pdf
Write the product as a sum or difference. Write the product as a sum.pdfWrite the product as a sum or difference. Write the product as a sum.pdf
Write the product as a sum or difference. Write the product as a sum.pdf
 
Which osmotic and ionic strategies must marine teleost fishes employ.pdf
Which osmotic and ionic strategies must marine teleost fishes employ.pdfWhich osmotic and ionic strategies must marine teleost fishes employ.pdf
Which osmotic and ionic strategies must marine teleost fishes employ.pdf
 
What types of social and culture trends affect REISolution1. .pdf
What types of social and culture trends affect REISolution1. .pdfWhat types of social and culture trends affect REISolution1. .pdf
What types of social and culture trends affect REISolution1. .pdf
 
Which of the following are in the order Primates (Multiple answers).pdf
Which of the following are in the order Primates (Multiple answers).pdfWhich of the following are in the order Primates (Multiple answers).pdf
Which of the following are in the order Primates (Multiple answers).pdf
 
What are the issues and benefits of employing older workers Wh.pdf
What are the issues and benefits of employing older workers Wh.pdfWhat are the issues and benefits of employing older workers Wh.pdf
What are the issues and benefits of employing older workers Wh.pdf
 
What is current I1What is current I2What is current I3 14 V 1.pdf
What is current I1What is current I2What is current I3 14 V 1.pdfWhat is current I1What is current I2What is current I3 14 V 1.pdf
What is current I1What is current I2What is current I3 14 V 1.pdf
 
Use your thoughts about the essay, , and your own reflections on y.pdf
Use your thoughts about the essay, , and your own reflections on y.pdfUse your thoughts about the essay, , and your own reflections on y.pdf
Use your thoughts about the essay, , and your own reflections on y.pdf
 
12-1 Group Work Preliminary and Program Development ResearchPurp.pdf
12-1 Group Work Preliminary and Program Development ResearchPurp.pdf12-1 Group Work Preliminary and Program Development ResearchPurp.pdf
12-1 Group Work Preliminary and Program Development ResearchPurp.pdf
 
This homework consists of 8 problems. The first 7ask that .pdf
This homework consists of 8 problems. The first 7ask that .pdfThis homework consists of 8 problems. The first 7ask that .pdf
This homework consists of 8 problems. The first 7ask that .pdf
 
this is verilog HDL classWhat are the basic components of a module.pdf
this is verilog HDL classWhat are the basic components of a module.pdfthis is verilog HDL classWhat are the basic components of a module.pdf
this is verilog HDL classWhat are the basic components of a module.pdf
 
The Hox genes are responsible for determining the anterior-posterior.pdf
The Hox genes are responsible for determining the anterior-posterior.pdfThe Hox genes are responsible for determining the anterior-posterior.pdf
The Hox genes are responsible for determining the anterior-posterior.pdf
 
The age of fossils can sometimes be determined by radiometric dating,.pdf
The age of fossils can sometimes be determined by radiometric dating,.pdfThe age of fossils can sometimes be determined by radiometric dating,.pdf
The age of fossils can sometimes be determined by radiometric dating,.pdf
 
Simple java programTopic Binary File IOCreate a simple applic.pdf
Simple java programTopic Binary File IOCreate a simple applic.pdfSimple java programTopic Binary File IOCreate a simple applic.pdf
Simple java programTopic Binary File IOCreate a simple applic.pdf
 
READ BEFORE YOU START You are given a partially completed pr.pdf
READ BEFORE YOU START  You are given a partially completed pr.pdfREAD BEFORE YOU START  You are given a partially completed pr.pdf
READ BEFORE YOU START You are given a partially completed pr.pdf
 
Select oneYes, because the correlation appears to be strong.No,.pdf
Select oneYes, because the correlation appears to be strong.No,.pdfSelect oneYes, because the correlation appears to be strong.No,.pdf
Select oneYes, because the correlation appears to be strong.No,.pdf
 
1) What data structure will you use for iterative post-order tree tr.pdf
1) What data structure will you use for iterative post-order tree tr.pdf1) What data structure will you use for iterative post-order tree tr.pdf
1) What data structure will you use for iterative post-order tree tr.pdf
 
Other diseases, called collagen vascular diseases, affect the protein.pdf
Other diseases, called collagen vascular diseases, affect the protein.pdfOther diseases, called collagen vascular diseases, affect the protein.pdf
Other diseases, called collagen vascular diseases, affect the protein.pdf
 
Discuss the origins of mitochondria and chloroplasts. Look at them i.pdf
Discuss the origins of mitochondria and chloroplasts. Look at them i.pdfDiscuss the origins of mitochondria and chloroplasts. Look at them i.pdf
Discuss the origins of mitochondria and chloroplasts. Look at them i.pdf
 
Match the following 1. Natural killer cells2. B cells3. Cy.pdf
Match the following 1. Natural killer cells2. B cells3. Cy.pdfMatch the following 1. Natural killer cells2. B cells3. Cy.pdf
Match the following 1. Natural killer cells2. B cells3. Cy.pdf
 

Recently uploaded

會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
中 央社
 
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPSSpellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
AnaAcapella
 
SURVEY I created for uni project research
SURVEY I created for uni project researchSURVEY I created for uni project research
SURVEY I created for uni project research
CaitlinCummins3
 

Recently uploaded (20)

How To Create Editable Tree View in Odoo 17
How To Create Editable Tree View in Odoo 17How To Create Editable Tree View in Odoo 17
How To Create Editable Tree View in Odoo 17
 
UChicago CMSC 23320 - The Best Commit Messages of 2024
UChicago CMSC 23320 - The Best Commit Messages of 2024UChicago CMSC 23320 - The Best Commit Messages of 2024
UChicago CMSC 23320 - The Best Commit Messages of 2024
 
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
24 ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH SỞ GIÁO DỤC HẢI DƯ...
 
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽會考英聽
 
ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...
ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...
ĐỀ THAM KHẢO KÌ THI TUYỂN SINH VÀO LỚP 10 MÔN TIẾNG ANH FORM 50 CÂU TRẮC NGHI...
 
FICTIONAL SALESMAN/SALESMAN SNSW 2024.pdf
FICTIONAL SALESMAN/SALESMAN SNSW 2024.pdfFICTIONAL SALESMAN/SALESMAN SNSW 2024.pdf
FICTIONAL SALESMAN/SALESMAN SNSW 2024.pdf
 
How to Send Pro Forma Invoice to Your Customers in Odoo 17
How to Send Pro Forma Invoice to Your Customers in Odoo 17How to Send Pro Forma Invoice to Your Customers in Odoo 17
How to Send Pro Forma Invoice to Your Customers in Odoo 17
 
Trauma-Informed Leadership - Five Practical Principles
Trauma-Informed Leadership - Five Practical PrinciplesTrauma-Informed Leadership - Five Practical Principles
Trauma-Informed Leadership - Five Practical Principles
 
Basic Civil Engineering notes on Transportation Engineering & Modes of Transport
Basic Civil Engineering notes on Transportation Engineering & Modes of TransportBasic Civil Engineering notes on Transportation Engineering & Modes of Transport
Basic Civil Engineering notes on Transportation Engineering & Modes of Transport
 
Mattingly "AI and Prompt Design: LLMs with NER"
Mattingly "AI and Prompt Design: LLMs with NER"Mattingly "AI and Prompt Design: LLMs with NER"
Mattingly "AI and Prompt Design: LLMs with NER"
 
An Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge AppAn Overview of the Odoo 17 Knowledge App
An Overview of the Odoo 17 Knowledge App
 
Mattingly "AI & Prompt Design: Named Entity Recognition"
Mattingly "AI & Prompt Design: Named Entity Recognition"Mattingly "AI & Prompt Design: Named Entity Recognition"
Mattingly "AI & Prompt Design: Named Entity Recognition"
 
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPSSpellings Wk 4 and Wk 5 for Grade 4 at CAPS
Spellings Wk 4 and Wk 5 for Grade 4 at CAPS
 
Supporting Newcomer Multilingual Learners
Supporting Newcomer  Multilingual LearnersSupporting Newcomer  Multilingual Learners
Supporting Newcomer Multilingual Learners
 
When Quality Assurance Meets Innovation in Higher Education - Report launch w...
When Quality Assurance Meets Innovation in Higher Education - Report launch w...When Quality Assurance Meets Innovation in Higher Education - Report launch w...
When Quality Assurance Meets Innovation in Higher Education - Report launch w...
 
AIM of Education-Teachers Training-2024.ppt
AIM of Education-Teachers Training-2024.pptAIM of Education-Teachers Training-2024.ppt
AIM of Education-Teachers Training-2024.ppt
 
8 Tips for Effective Working Capital Management
8 Tips for Effective Working Capital Management8 Tips for Effective Working Capital Management
8 Tips for Effective Working Capital Management
 
OSCM Unit 2_Operations Processes & Systems
OSCM Unit 2_Operations Processes & SystemsOSCM Unit 2_Operations Processes & Systems
OSCM Unit 2_Operations Processes & Systems
 
SURVEY I created for uni project research
SURVEY I created for uni project researchSURVEY I created for uni project research
SURVEY I created for uni project research
 
Book Review of Run For Your Life Powerpoint
Book Review of Run For Your Life PowerpointBook Review of Run For Your Life Powerpoint
Book Review of Run For Your Life Powerpoint
 

Prove the hyperbolic function formula sinhx(2x)=2sinhxcoshxSol.pdf

  • 1. Prove the hyperbolic function formula: sinhx(2x)=2sinhxcoshx Solution Just use the definitions of sinh(x) and cosh(x): sinh(x) = [e^x - e^(-x)]/2, cosh(x) = [e^x + e^(-x)]/2 So, simply expand! sinh(2x) = [e^(2x) - e^(-2x)]/2 = [e^x - e^(-x)][e^x + e^(- x)]/2 = 2 [[e^x - e^(-x)]/2][[e^x + e^(-x)]/2] = 2sinh(x)cosh(x)