Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • What is the maximum value of the function sin x + cos x?

9. What is the maximum value of the function \sin x + \cos x

Answers (1)

best_answer

Given function is 
f(x) = \sin x + \cos x
f^{'}(x) = \cos x - \sin x\\ f^{'}(x)= 0\\ \cos x- \sin x= 0\\ \cos = \sin x\\ x = 2n\pi+\frac{\pi}{4} \ where \ n \ \epsilon \ I       
Hence, x = 2n\pi+\frac{\pi}{4} is the critical point  of the function f(x) = \sin x + \cos x
Now, we need to check the value of the function f(x) = \sin x + \cos x  at x = 2n\pi+\frac{\pi}{4} 
Value is same for all cases so let assume that n = 0
Now
f(\frac{\pi}{4}) = \sin \frac{\pi}{4} + \cos \frac{\pi}{4}\\
            =\frac{1}{\sqrt2}+\frac{1}{\sqrt2} = \frac{2}{\sqrt2} = \sqrt2


Hence, the maximum value of the function f(x) = \sin x + \cos x  is \sqrt2
 

Posted by

Gautam harsolia

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board Exams 2025: Guidelines issued for Class 10, 12 practicals
anam-khan

Board Exam Date Sheet 2025 Live: ICSE, ISC, CBSE, MP time table out; BSEB routine soon
anam-khan

Board exam dates 2025: CBSE, CISCE, UP, MP, Maharashtra, TN time table out; state-wise updates

Latest Question