$\sin h [x + \frac{π i}{2}] =$

$i \cos h x$

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$- i \cos h x$

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$\cos x$

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$- \cos x$

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Solution

The correct option is A
$i \cos h x$

Explanation for the correct answer:
Simplifying the given expression using trigonometric identities:
Given
$\sin h [x + \frac{π i}{2}] = - i \sin [i x + \frac{π}{2}] = i \sin [\frac{π}{2} - i x] = i \cos (i x) [∵ \sin [\frac{π}{2} - θ] = \cos θ] = i \cos h x$
Thus, $\sin h [x + \frac{π i}{2}] =$ $i \cos h x$
Therefore, option (A) is the correct answer.

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