A) \[\left( \frac{3}{5},\,\frac{4}{5} \right)\]
B) \[\left( \sqrt{3},\frac{1}{\sqrt{3}} \right)\]
C) \[\left( \sqrt{\frac{\sqrt{5}-1}{2}},\sqrt{\frac{\sqrt{5}-1}{2}} \right)\]
D) \[\left( \sqrt{\frac{\sqrt{3}-1}{2}},\sqrt{\frac{\sqrt{3}-1}{2}} \right)\]
Correct Answer: A
Solution :
\[\because \] b, c and a are in AP. \[\therefore \]\[\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\] \[\Rightarrow \] \[a=\frac{b}{\sin B}=\frac{c}{\sin C}\] \[(\because \angle A=90{}^\circ )\] \[\Rightarrow \] \[\sin B=\frac{b}{a},\]\[\sin C=\frac{c}{a}\] Hence, option [a] satisfies this equation.
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