MCQ
In a $\triangle ABC , 2 ac \sin \left(\frac{ A - B + C }{2}\right)$ is equal to
- A$a^2+b^2-c^2$
- ✓$c^2+a^2-b^2$
- C$b^2-c^2-a^2$
- D$c^2-a^2-b^2$
✓
Answer
Correct option: B.
$c^2+a^2-b^2$
(B) $2 ac \sin \frac{ A - B + C }{2}=2 ac \sin \frac{\pi-2 B}{2}$
$=2 ac \cos B$
$=2 ac \frac{ c ^2+ a ^2- b ^2}{2 ca }$ …..[By cosine rule]
$= c ^2+ a ^2- b ^2$
$=2 ac \cos B$
$=2 ac \frac{ c ^2+ a ^2- b ^2}{2 ca }$ …..[By cosine rule]
$= c ^2+ a ^2- b ^2$
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