Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove that the function f given by f (x) = log sin x is increasing on 0, 2 pi and decreasing on pi by 2 ,pie

16) Prove that the function f given by f (x) = \log \sin x  is increasing on 

\left ( 0 , \pi /2 \right )\: \: and \: \: decreasing \: \: on \: \: \left ( \pi/2 , \pi \right )
 

Answers (1)

best_answer

Given function is,
f (x) = \log \sin x
f^{'}(x) = \frac{1}{\sin x}\cos x = \cot x
Now, we know that  cot x is+ve in the interval  \left ( 0 , \pi /2 \right )   and -ve  in the interval \left ( \pi/2 , \pi \right )
f^{'}(x) > 0 \ in \ \left ( 0,\frac{\pi}{2} \right ) \ and \ f^{'}(x) < 0 \ in \ \left ( \frac{\pi}{2} , \pi \right )
Hence, f (x) = \log \sin x  is increasing in the interval \left ( 0 , \pi /2 \right ) and   decreasing in interval  \left ( \pi/2 , \pi \right )

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 Supplementary Exam 2025: Registrations open for Class 10, 12 private students today
anam-khan

CBSE opens application to access 10th answer scripts; verification, revaluation for Class 12 starts on May 31
anam-khan

CBSE supplementary exams 2025 from July 15; form submission starts on May 30

Latest Question