find the simplest value of (cos A + sin A)2 + (sin A - cos A)2???
Answers
Step-by-step explanation:
eNotes HomeHomework HelpStudy GuidesTextsTeachers▻Sign InJoin
rowseNotessearch
Math Questions and Answers
MENU
Prove that (sin A - cos A + 1)/(sin A + cos A - 1) =cos A/1-sin A THIS QUESTION IS FROM CHAPTER TRIGNOMETRIC IDENTITIES AND IN THIS QUESTION WE HAVE TO PROVE THE LEFT HAND SIDE=RIGHT HAND SIDE.
print Print document PDF list Cite
Expert Answers info
TUSHAR CHANDRA | CERTIFIED EDUCATOR
We have to prove that (sin A - cos A + 1)/(sin A + cos A - 1) = cos A/(1 - sin A)
Start from the left hand side
(sin A - cos A + 1)/(sin A + cos A - 1)
=> (sin A - cos A + 1)(sin A - cos A -1)/(sin A + cos A - 1)(sin A - cos A -1)
=> ((sin A - cos A)^2 - 1)/((sin A - 1)^2 - (cos A)^2)
=> ((sin A - cos A)^2 - 1)/((sin A)^2 - 2*sin A + 1 - (cos A)^2)
=> ((sin A - cos A)^2 - 1)/((sin A)^2 - 2*sin A + (sin A)^2)
=> ((sin A)^2 + (cos A)^2 - 2*sin A*cos A - 1)/((sin A)^2 - 2*sin A + (sin A)^2)
=> (1- 2*sin A*cos A - 1)/((sin A)^2 - 2*sin A + (sin A)^2)
=> (-2*sin A*cos A)/(2*(sin A)^2 - 2*sin A)
=> (-cos A)/(sin A - 1)
=> cos A/(1 - sin A)
which is the right hand side
This proves:(sin A - cos A + 1)/(sin A + cos A - 1) = cos A/(1 - sin A)
check Approved by eNotes Editorial
list Cite link Link
Related QuestionsHow to prove the identity ?3 EDUCATOR ANSWERSHow to prove the identity sin^2x + cos^2x = 1 ?1 EDUCATOR ANSWERProve tan x + cos x/(1+sin x) = 1/cos x1 EDUCATOR ANSWERProve the following identity 1-2sin^2a=cos^4a-sin^4a.2 EDUCATOR ANSWERSProve the identity sin x - sin y = 2 sin( (x - y)/2 ) cos( (x + y)/2 )?2 EDUCATOR ANSWERS
More »
We'll Help Your Grades Soar
Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.
300,000+ answers30,000+ book summaries20% study tools discountAd-free contentPDF downloads5-star customer support
Start 48-Hour Free Trial
Already a member? Log in here.
Student Answers
Ask a Question
Popular QuestionsWhat do the letters R, Q, N, and Z mean in math?1 EDUCATOR ANSWERHow do I determine if this equation is a linear function or a nonlinear function?8 EDUCATOR ANSWERSGiven f(x) and g(x), please find (fog)(X) and (gof)(x) f(x) = 2x g(x) = x+31 EDUCATOR ANSWER1. When 2 dice at thrown, what is the probability of the sum being 9? 2. Two cards are picked at...1 EDUCATOR ANSWERDetermine if its a growth or decay.Then find the percent increase of decrease. 1.y=16(.25)^x...1 EDUCATOR ANSWER
More »
eNotes.com will help you with any book or any question. Our summaries and analyses are written by experts, and your questions are answered by real teachers.
Join eNotes
Apply to be an Educator
RecommendedLiterature Study GuidesNew Study GuidesLiterature Lesson PlansShakespeare QuotesHomework HelpLiterary TermsiOS AppAndroid AppOther Useful StuffFAQAbout UsContact UsPrivacy PolicyTerms of UseJobsBlogConnect With Us
© 2020 eNotes.com, Inc. All Rights Reserved.