GATE 2025 AG – Question 13
$s/(s^2+a^2)$ is the Laplace transform of which function of t?
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Correct answer: (A) $\cos at$
Explanation
The standard transform $\int_0^\infty e^{-st}\cos(at)dt=s/(s^2+a^2)$ follows by taking the real part of $1/(s-ia)$. Sine instead has numerator a, and hyperbolic transforms have denominator $s^2-a^2$. Thus **A**.