logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
0 votes

If $\cos^{-1}x=\tan^{-1}x,\;show\;that\;\sin(\cos^{-1}x)=x^2$

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • \( cos^{-1}x = tan^{-1} \large\frac{\sqrt{1-x^2}}{x} \)
  • \( sincos^{-1}x=\sqrt{1-x^2}\)
given \( cos^{-1}x=tan^{-1}x\)
 
By substituting the above formula of \(cos^{-1}x\)
\( \Rightarrow tan^{-1} \large\frac{\sqrt{1-x^2}}{x}=tan^{-1}x\)
\( \Rightarrow \large\frac{ \sqrt{1-x^2}}{x}=x\)
\( \Rightarrow \sqrt{1-x^2}=x^2\)
 
Now \( sin\: cos^{-1}x = \sqrt{1-x^2}=x^2\)

 

answered Feb 20, 2013 by thanvigandhi_1
edited Mar 19, 2013 by thanvigandhi_1
 

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
...