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Question

If 2sinh1(a1a2)=log(1+x1x), then x=

A
a
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B
1a
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C
1a2
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D
11a2
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Solution

The correct option is A a
As we know that
sinh1x=log(x+x2+1)
2sinh1(a1a2)=2log(a1a2+a21a2+1)
=2log(a+a2+1a21a2)
=2log(a+11a2)
=log((1+a)2(1a)(1+a))
=log(1+a1a)
But given 2sinh1(a1a2)=log(1+x1x)
So x=a

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