find the numerical valuesinh^(-1)1 ......................sinh to the negative one power of one

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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let `sinh^-1 (1)= x`

==> sinh(x)= 1

But we know that:

`sinh(x)= (e^(2x) -1)/(2e^x) = 1 `

`==gt e^2x -1 = 2e^x `

`==gt e^2x - 2e^x -1 = 0 `

`==gt e^x = (2+-sqrt(8))/2 `

`==gt e^x = 1+-sqrt2`

`==gt x= ln (1+-sqrt2) `

`==gt x = ln(1+sqrt2)= ln(2.41)=0.8814`

`==gt x = ln(1-sqrt2) ` ==> Not valid.

==> x = 0.8814  

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