Ask Questions, Get Answers

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

If the angles $A,B,C$ of a $\Delta$le are in arithmetic progression and if $a,b$ and $c$ denote the lengths of the sides opposite to $A,B$ and $C$ respectively,then the value of the expression $\large\frac{a}{c}$$\sin 2C+\large\frac{c}{a}$$\sin 2A$ is

$(a)\;\large\frac{1}{2}$$\qquad(b)\;\large\frac{\sqrt 3}{2}$$\qquad(c)\;1\qquad(d)\;\sqrt 3$

Can you answer this question?

1 Answer

0 votes
Since $A,B,C$ are in AP
$\Rightarrow 2B=A+C$
(i.e) $\sqrt B=60^{\large\circ}$
$\therefore \large\frac{a}{c}$$(2\sin C\cos C)+\large\frac{C}{a}$$(2\sin A\cos A)=2k(a\cos C+C\cos A)$
$\big[Using\;\large\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{C}{\sin C}=\frac{1}{k}\big]$
$\Rightarrow 2k(b)$
[Using $b=a\cos C+c\cos A$]
$\Rightarrow 2\sin B$
$\Rightarrow \sqrt 3$
Hence (d) is the correct answer.
answered Oct 10, 2013 by sreemathi.v

Related questions

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