sin4x+Cos4x?

Asked by Last Modified  

31 Answers

Learn Class XI-XII Tuition (PUC)

Follow 0
Answer

Please enter your answer

K Bala Krishna

Math & Science Tutor

We Know that, Sin^2(x) + Cos^2(x) = 1 Squaring on both sides Sin^4(x) + Cos^4(x) + 2Sin^2(x)Cos^2(x) = 1 {Using (a + b)^2 = a^2 + b^2 + 2ab } Sin^4(x) + Cos^4(x) = 1 - 2Sin^2(x)Cos^2(x)
Comments
Dislike Bookmark

Trainer

sinx)^4+(cosx)^4 = 1 The soltion is obvious but a procedure is as below: s^4+(1-s^2)^2 = 1, where s = sinx. Also (sinx)^2+(cosx)^2 = 1 is a trigonometric identity for all x. So, (cosx)^4 = ^2 = (1-s^2)^2. Therefore, s^4+1-2s^2+s^4=1 2s^4-2s^2=0 s^4-s^2 = 0 s^2(s^2-1)=0 s^2 = 0 or s^2 = 1 s=0...
read more
sinx)^4+(cosx)^4 = 1 The soltion is obvious but a procedure is as below: s^4+(1-s^2)^2 = 1, where s = sinx. Also (sinx)^2+(cosx)^2 = 1 is a trigonometric identity for all x. So, (cosx)^4 = [(cosx)^2]^2 = (1-s^2)^2. Therefore, s^4+1-2s^2+s^4=1 2s^4-2s^2=0 s^4-s^2 = 0 s^2(s^2-1)=0 s^2 = 0 or s^2 = 1 s=0 or s=1 or s=-1 read less
Comments
Dislike Bookmark

Tutor

sin(4x) = 2 sin(2x) cos(2x) 2 (2 sin(x) cos(x)) (cos²(x) - sin²(x)) 4 sin(x) cos(x) (cos²(x) - sin²(x)) 4 sin(x) cos³(x) - 4 sin³(x) cos(x) -------eq 1 cos(4x) 2cos^2(2x) - 1 2^2 - 1 8cos^4(x) - 8cos^2(x) + 1 -------eq 2 Add both eq1 and eq2 solve the equation in such way you want a...
read more
sin(4x) = 2 sin(2x) cos(2x) 2 (2 sin(x) cos(x)) (cos²(x) - sin²(x)) 4 sin(x) cos(x) (cos²(x) - sin²(x)) 4 sin(x) cos³(x) - 4 sin³(x) cos(x) -------eq 1 cos(4x) 2cos^2(2x) - 1 2[2cos^2(x) - 1]^2 - 1 8cos^4(x) - 8cos^2(x) + 1 -------eq 2 Add both eq1 and eq2 solve the equation in such way you want answer. read less
Comments
Dislike Bookmark

Tutor

In trigonometry and in more parts of mathematics, you can not ask how much this will be as you can get and no of solutions for the same expression. So you may ask how to get the required once if you wont get that one. Please try to understand. Here we can see the above answers as well. they all are right...
read more
In trigonometry and in more parts of mathematics, you can not ask how much this will be as you can get and no of solutions for the same expression. So you may ask how to get the required once if you wont get that one. Please try to understand. Here we can see the above answers as well. they all are right in their own way. So what answer you need is important that too in mathematics. Thanks. read less
Comments
Dislike Bookmark

Tutor

1. Integration by parts 2. u-substitution 3. Reverse chain rule 4. Partial fraction expansion 5. Integration using trigonometric identities 6. Trigonometric substitution
Comments
Dislike Bookmark

Maths Teacher

1
Comments
Dislike Bookmark
Dr S, please check your expansion of Cos 2x. You have expanded cos 2x as cos^2 2x - sin^2 2x which is wrong. Mistake could be by oversight. Sorry for pointing out.
Comments
Dislike Bookmark
K Bala, the question seems to be sin 4x + cos 4x but you have solved for Sin^4 x + cos^4 x.
Comments
Dislike Bookmark

Tutor

U-substitution Double u-substitution Partial fractions Inverse trig functions Improper integrals Impossible integrals Powers of sine/cosine u/dv tabular Integration by parts
Comments
Dislike Bookmark

Tuition

-1.
Comments
Dislike Bookmark

View 29 more Answers

Related Questions

When an electron in hydrogen atom jumps from higher orbit into third orbit. The set of lines emitted is called __________. (Balmer Series, Lyman Series, Bracket Series, Paschen Series)
Paschen Series
Narendra Kumar
0 0
9
The amount of heat required to raise the temperature of 2.0 x 108kg of water from 0°C to 100°C is equal to __________. (9 x 1013J, 9 x 1012J, 9 x 1011J, 9 x 1010J)
Q=mc?T, where Q= amount oh heat required to raise the temperature by ?T c- specific heat capacity of the substance ?T- Temperature difference m-mass of the substance So,...
Narendra Kumar
0 0
7
Conductors have a high or low resistance?
Low resistance
Sugantha
The concepts of electric field lines was introduced by a famous scientist __________ (Newton, Faraday, Einstein, Coulomb)
Faraday
Narendra Kumar
0 0
6
A motor boat whose speed is 18km/h in still water take 1 hour more to go 24km upstream than to return down stream to the same spot. find the speed of stream
Given, speed of the boat in still water = 18 km/hr. Let the speed of the stream be x km/hr. Speed of the boat upstream = Speed of boat in still water -- Speed of the stream ? Speed of the boat...
Sandeep

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

I just talk with chalk
Do quality study ...don't focus on hours jst focus on wat u gain in those hours...and don't just read have a vision to imagine ..make ur dreams solve ur problems

Radhika Sarda

0 0
0
Jaliya Maradante - Shabdhartha

Sandhya

1 0
0
False benefits & advantages of English language labs.
False benefits & advantages of language labs. The number of schools using language labs has increased noticeably. This paper is aimed at discussing the real &...

Readmyscript Outreach Program

0 0
0
GST News, Notifications And Announcements
Central Tax Notifications: Composition Scheme- Notification 3 & 8/2017: Composition scheme threshold has been notified to be 75 lakhs (earlier recommended only). This will be beneficial to small...

FR Prashanth Reddy

5 Tips For College Students
Here are 5 tips to help the college students to create a productive & memorable college experience: (1) Answer the question ," Why am I going to college?" : Many college students really don't have...

Amathul Noor

0 0
0

Recommended Articles

Meet Swati, a Hindi Tutor from Bangalore

Swati is a renowned Hindi tutor with 7 years of experience in teaching. She conducts classes for various students ranging from class 6- class 12 and also BA students. Having pursued her education at Madras University where she did her Masters in Hindi, Swati knows her way around students. She believes that each student...

Read full article >

Meet Radhe Shyam Burman, an MBA Tutor from...

Radhe Shyam is a highly skilled accounts and finance trainer with 8 years of experience in teaching. Accounting is challenging for many students and that’s where Radhe Shyam’s expertise comes into play. He helps his students not only in understanding the subject but also advises them on how to overcome the fear of accounts...

Read full article >

Meet Urmila, an MBBS tutor from Bangalore

Urmila is a passionate teacher with over 8 years of experience in teaching. She is currently pursuing her Ph. D. She provides classes for Class 11, Class 12, MBBS and Medical tuition.  Urmila began her career in teaching long before she became a teacher. She used to provide classes for foreign national students in her college...

Read full article >

Meet Sandhya R, a B.Sc tutor from Bangalore

Sandhya is a proactive educationalist. She conducts classes for CBSE, PUC, ICSE, I.B. and IGCSE. Having a 6-year experience in teaching, she connects with her students and provides tutoring as per their understanding. She mentors her students personally and strives them to achieve their goals with ease. Being an enthusiastic...

Read full article >

Find Class 12 Tuition near you
Class 12 Tuition in Delhi
Class 12 Tuition in Bangalore
Class 12 Tuition in Chennai
Class 12 Tuition in Hyderabad
Class 12 Tuition in Kolkata
Class 12 Tuition in Mumbai
Class 12 Tuition in Pune
Class 12 Tuition in Lucknow
Class 12 Tuition in Noida
Class 12 Tuition in Gurgaon
Online Tuition Class 12

Looking for Class 12 Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you