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AP DSC School Assistant Math Model Test 2

Section: Subject Specific

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Question : 106 of 160

Marks: +1, -0

sin h^{-1} 3 = _______

$log(3+\sqrt{10})$
$log(3-2\sqrt{2})$
$log(3+2\sqrt{2})$
None of these

Solution:

Concept:

The inverse hyperbolic sine function is defined as

\sinh^{-1} x = \log\left(x + \sqrt{x^2 + 1}\right)

for all real

x

.

Explanation:

We need to evaluate

\sinh^{-1} 3

. Using the definition, substitute

x = 3

:

\sinh^{-1} 3 = \log\left(3 + \sqrt{3^2 + 1}\right) = \log\left(3 + \sqrt{9 + 1}\right) = \log(3 + \sqrt{10})

.

Answer:

Option A:

\log(3+\sqrt{10})

is correct.

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