54. If e* = y + 1+ y2, then y = (c)...
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54. If e* = y + 1+ y2, then y = (c) e ter (d) e-e

JEE/Engineering Exams
Maths
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( e^{x}=y+sqrt{1+y^{2}} ) ( Rightarrow sqrt{1+y^{2}=}=frac{e^{x}-y}{e^{2 x}-2 y e^{x}+y^{2}} ) ( quad 1+y^{2}=quad y e^{x}=e^{2 x}-1 ) ( Rightarrow y=frac{e^{2 x}-1}{2 e^{x}}=frac{e^{x}-e^{-x}}{2} )
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