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 $\cos[2\tan^{-1}(-7)]$ is

$(a)\;\large\frac{49}{50}$$\qquad(b)\;\large\frac{-49}{50}$$\qquad(c)\;\large\frac{24}{25}$$\qquad(d)\;-\large\frac{24}{25}$

Can you answer this question?
 
 

1 Answer

0 votes
$\cos(2\tan^{-1}(-7))=\cos\big[\cos^{-1}\big(\large\frac{1-49}{1+49}\big)\big]$
$\qquad\qquad\qquad\;\;=\cos\big[\cos^{-1}\big(\large\frac{-48}{50}\big)\big]$
$\qquad\qquad\qquad\;\;=\cos\big[\pi-\cos^{-1}\big(\large\frac{48}{50}\big)\big]$
$\qquad\qquad\qquad\;\;=\cos\big[-\cos^{-1}\big(\large\frac{48}{50}\big)\big]$
$\qquad\qquad\qquad\;\;=-\cos\cos^{-1}\big(\large\frac{48}{50}\big)$
$\qquad\qquad\qquad\;\;=\large\frac{-48}{50}$
$\qquad\qquad\qquad\;\;=\large\frac{-24}{25}$
Hence (d) 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
...