A) \[\frac{\Delta }{2}\]
B) \[\Delta \]
C) \[2\Delta \]
D) \[3\Delta \]
E) \[4\Delta \]
Correct Answer: E
Solution :
\[{{c}^{2}}sin\text{ }2B+{{b}^{2}}sin\text{ }2C\] \[={{c}^{2}}(2sinB\,cosB)+{{b}^{2}}(2sinC\,cosC)\] \[=2{{c}^{2}}\left( \frac{2\Delta }{ac}\cos B \right)+2{{b}^{2}}\left( \frac{2\Delta }{ab}\cos C \right)\] \[=4\Delta \left( \frac{c\cos B+b\cos C}{a} \right)\] \[=4\Delta \left( \frac{a}{a} \right)=4\Delta \]
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