A) \[3+\sqrt{5}\]
B) \[\frac{2+\sqrt{5}}{2\sqrt{5}}\]
C) \[2+\sqrt{5}\]
D) \[3\sqrt{5}\]
Correct Answer: B
Solution :
\[\frac{AB}{BC}=\frac{2}{1}\] \[\Rightarrow AB=2k,BC=k\] \[\therefore AC=\sqrt{{{(2k)}^{2}}+{{k}^{2}}}=\sqrt{5{{k}^{2}}}=\sqrt{5k}\] \[\therefore \] sin A + cot C=\[\frac{BC}{AC}+\frac{BC}{AB}=\frac{K}{\sqrt{5}k}+\frac{k}{2k}\] \[=\frac{1}{\sqrt{5}}+\frac{1}{2}=\frac{2+\sqrt{5}}{2\sqrt{5}}\]You need to login to perform this action.
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