Ask Questions, Get Answers

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

If $A+B+C=\pi$ then $\sin 2A+\sin 2B+\sin 2C$ is equal to

$\begin{array}{1 1}(a)\;4\sin A\sin B\sin C&(b)\;\sin A\sin B\sin C\\(c)\;2\sin A\sin B\sin C&(d)\;None\;of\;these\end{array}$

Can you answer this question?

1 Answer

0 votes
We have :-
$\sin 2A+\sin 2B+\sin 2C$
$\Rightarrow (\sin 2A+\sin 2B)+\sin 2C$
$\Rightarrow 2\sin\big(\large\frac{2A+2B}{2}\big)$$\cos\big(\large\frac{2A-2B}{2}\big)$$+\sin 2C$
$\Rightarrow 2\sin(A+B)\cos(A-B)+\sin 2C$
$\Rightarrow 2\sin C\cos(A-B)+2\sin C\cos C$
We have $A+B+C=\pi$
$\Rightarrow 2\sin C[\cos(A-B)+\cos C]$
$\Rightarrow 2\sin C[\cos(A-B)-\cos(A+B)]$
$\Rightarrow 2\sin C(2\sin A\sin B)$
$\Rightarrow 4\sin A\sin B\sin C$
Hence (a) is the correct option.
answered Oct 15, 2013 by sreemathi.v

Related questions

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