A) \[{{e}^{x}}-{{e}^{-x}}\]
B) \[\frac{1}{2}({{e}^{x}}-{{e}^{-x}})\]
C) \[{{e}^{x}}+{{e}^{-x}}\]
D) None of these
Correct Answer: B
Solution :
Given equation can be rewritten as \[{{e}^{x}}-y=\sqrt{1+{{y}^{2}}}\] On squaring both sides, we get \[{{e}^{2x}}+{{y}^{2}}-2y{{e}^{x}}=1+{{y}^{2}}\] \[\Rightarrow \] \[{{e}^{2x}}-2y{{e}^{x}}=1\] \[\Rightarrow \] \[2y{{e}^{x}}={{e}^{2x}}-1\] \[\Rightarrow \] \[y=\frac{{{e}^{x}}-{{e}^{-x}}}{2}\]
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