A) 0
B) 1
C) b
D) 2b
Correct Answer: D
Solution :
\[\angle C={{180}^{o}}-{{45}^{o}}-{{75}^{o}}={{60}^{o}}\] Therefore \[a+c\sqrt{2}=k(\sin A+\sqrt{2}\sin C)\] = \[k\,\left( \frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{2}\sqrt{2} \right)=k\,\left( \frac{1+\sqrt{3}}{\sqrt{2}} \right)\] and \[k=\frac{b}{\sin B}\Rightarrow a+c\sqrt{2}=\frac{b}{\sin {{75}^{o}}}\left( \frac{1+\sqrt{3}}{\sqrt{2}} \right)=2b\].
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