logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
0 votes

The value of $x$ satisfying $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$ are

$(a)\;0,\large\frac{1}{2}$$\qquad(b)\;1,2\qquad(c)\;0,2\qquad(d)\;None\;of\;these$

Can you answer this question?
 
 

1 Answer

0 votes
We have $\sin^{-1}x+\sin^{-1}(1-x)=\cos^{-1}x$
$\Rightarrow \large\frac{\pi}{2}$$-\cos^{-1}x+\large\frac{\pi}{2}$$-\cos^{-1}(1-x)=\cos^{-1}x$
$\Rightarrow 2\cos^{-1}x=\pi-\cos^{-1}(1-x)$
$\Rightarrow \cos^{-1}(2x^2-1)=\cos^{-1}(x-1)$
$\cos^{-1}(-x)=\pi-\cos^{-1}x$
$\Rightarrow 2x^2-1=x-1$
$\Rightarrow x(2x-1)=0$
$x=0$
$2x-1=0$
$2x=1$
$x=\large\frac{1}{2}$
$\therefore x=0,\large\frac{1}{2}$
Hence (a) is the correct answer.
answered Oct 11, 2013 by sreemathi.v
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...