Question

If the angles $A,B$ and $C$ of a triangle 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 $\frac{a}{c}\sin 2C+\frac{c}{a}\sin 2A$ is:

• A. $\frac{1}{2}$
• B. $\frac{\sqrt{3}}{2}$
• C. $1$
• D. $\sqrt{3}$

Answer 1

The correct option is D $\sqrt{3}$

Since angles of $\Delta ABC$ are in $A.P.$,
$2B=A+C$
Also , $A+B+C={180}^0$
$\therefore B={60}^0$
$\therefore \frac{a}{c}\sin 2C+\frac{c}{a}\sin 2A=2\sin A\cos C+2\sin C\cos A$
$=2\sin (A+C)=2\sin B=2\times \frac{\sqrt{3}}{2}=\sqrt{3}$