Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • If sin(sin inverse 1 / 5 + cos inverse x) = 1, then find the value of x.

14. If \sin\left(\sin^{-1}\frac{1}{5} + \cos ^{-1}x \right ) =1, then find the value of x.

Answers (1)

best_answer

As we know the identity;

 sin^{-1} x + cos^{-1} x = \frac {\pi}{2},\ x\ \epsilon\ [-1,1]. it will just hit you by practice to apply this.

So, \sin\left(\sin^{-1}\frac{1}{5} + \cos ^{-1}x \right ) =1     or    \sin^{-1}\frac{1}{5} + \cos ^{-1}x =\sin^{-1}(1),

we can then write \cos^{-1}x = \frac{\pi}{2} - \sin^{-1}x,

putting in above equation we get;

\sin^{-1}\frac{1}{5} + \frac{\pi}{2} - \sin^{-1}x =\frac{\pi}{2}                          \because \left [ \sin^{-1}(1)=\frac{\pi}{2} \right ]

= \sin^{-1}x = \sin^{-1} \frac{1}{5}  

Ans.x = \frac{1}{5}

 

Posted by

Divya Prakash Singh

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 reminds schools to submit registration data of Class 9, 11 students by October 16
anam-khan

CBSE reopens online portal for submission of LOC for Class 10, 12 board exams 2026; submit forms by Oct 8
anam-khan

CBSE private candidates challenge cancellation of post-Class 12 additional subject exam in Delhi HC

Latest Question