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

If $f(\theta)=(\sin\theta+cosec\theta)^2+(\cos\theta+\sec\theta)^2$ then minimum value of $f(\theta)$ is

$(a)\;\big[\large\frac{3}{2}$$,2\big]\qquad(b)\;\big[1,\large\frac{3}{2}\big]$$\qquad(c)\;[1,2]\qquad(d)\;None\;of\;these$

Can you answer this question?
 
 

1 Answer

0 votes
$f(\theta)=(\sin\theta+cosec\theta)^2+(\cos\theta+\sec\theta)^2$
$\Rightarrow \sin^2\theta+\cos^2\theta+cosec^2\theta+\sec^2\theta+4$
$\Rightarrow 5+\large\frac{1}{\sin^2\theta}+\frac{1}{\cos^2\theta}$
$\Rightarrow 5+\large\frac{4}{4\sin^2\theta\cos^2\theta}$
$\Rightarrow 5+\large\frac{4}{\sin^22\theta}$$\geq 9$
Hence (d) is the correct option.
answered Oct 9, 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
...