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

Engineering

Mathematics

Basic Rules of Properties of Triangle

Question

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

$\frac{\sqrt{3}}{2}$

$\frac{1}{2}$

$\sqrt{3}$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

= 2 sin(A + C) = 2 sin ( $π$ – B) = 2 sin B

As A + B + C = $π$ and A + C = 2B $\Rightarrow$ B = 60°

$∴$ E = 2 sin 60° = $2 (\frac{\sqrt{3}}{2}) = \sqrt{3}$ Ans.

Please subscribe our Youtube channel to unlock this solution.