A) \[\sqrt{2}\]
B) \[\frac{\sqrt{3}+1}{2}\]
C) \[\frac{\sqrt{3}-1}{2}\]
D) 1
Correct Answer: A
Solution :
\[a=3,b=5,c=4,\,\,s=\frac{a+b+c}{2}=\frac{12}{2}=6\] \[\sin \frac{B}{2}=\sqrt{\frac{(s-c)(s-a)}{ca}}=\sqrt{\frac{2.3}{12}}=\sqrt{\frac{1}{2}}\] \[\cos \frac{B}{2}=\sqrt{\frac{s(s-b)}{ca}}=\sqrt{\frac{6.1}{12}}=\sqrt{\frac{1}{2}}\] \\[\sin \frac{B}{2}+\cos \frac{B}{2}=\frac{2}{\sqrt{2}}=\sqrt{2}\].
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