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Question

lf y=12 cosech-1 (12X1+x2) , then x=

A
coshy
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B
sinhy
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C
tanhy
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D
cothy
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Solution

The correct option is A sinhy
Given y=12cosech1(12x1+x2)=12ln(1+1(14x2(1+x2))12x1+x2)
=12ln(4x2+4x41+2x1+x21)
e2y=4x2+4x41+2x2+x2
e2y=12x1+x24x4+4x21
2x1+x2=e2y+e2y2=cosh2y
and 4x4+4x21=e2ye2y2=sinh2y
4x4+4x2(1+sin2h2y)=0
4x4+4x2+cos2hy=0
x2=4±1616cos2hy8
x2=1±isinhy2

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