JEE Main & Advanced
Sample Paper
JEE Main - Mock Test - 13
question_answer
In \[\Delta ABC,\] the median divides \[\angle BAC\] such that \[\angle BAD:\angle CAD=2:1.\] Then the value of \[\cos \left( \frac{A}{3} \right)\]equals
A)\[\frac{\sin B}{2\sin C}\]
B) \[\frac{\sin \,C}{2\sin B}\]
C)\[\frac{2\sin \,B}{\sin \,C}\]
D) None of these
Correct Answer:
A
Solution :
[a] Using sine rule in \[\Delta ABD\] and \[\Delta ADC,\] we get \[\frac{AD}{\sin B}=\frac{BD}{\sin \frac{2A}{3}}\] and \[\frac{AD}{\sin \,\,C}=\frac{CD}{\sin \frac{A}{3}}\] \[\therefore \,\,\,\frac{\sin B}{\sin C}=\frac{\sin \frac{2A}{3}}{\sin \frac{A}{3}}\] \[(\because \,BD=CD)\] \[\therefore \,\,\,\,\cos \frac{A}{3}=\frac{\sin B}{2\sin C}\]