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Laplace transform of sin ht is

This question belongs to Engineering Maths Transform Theory
Transform Theory
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Laplace transform of sin ht is

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Correct Answer: Option A
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The Laplace transform F(s) of the exponential function. f(t) = eat when t ≥ 0, where a is a constant and (s - a) > 0, is
A. $$\frac{1}{{{\text{s}} + {\text{a}}}}$$ B. $$\frac{1}{{{\text{s}} - {\text{a}}}}$$ C. $$\frac{1}{{{\text{a}} - {\text{s}}}}$$ D. $$\infty $$
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If the Laplace transform of $${{\text{e}}^{\omega {\text{t}}}}$$  is $$\frac{1}{{{\text{s}} - \omega }},$$  the Laplace transform of tcosh t is
A. $$\frac{{1 + {{\text{s}}^2}}}{{{{\left( {{{\text{s}}^2} - 1} \right)}^2}}}$$ B. $$\frac{{{\text{st}}}}{{\left( {{{\text{s}}^2} - 1} \right)}}$$ C. $$\frac{{1 - {{\text{s}}^2}}}{{{{\left( {{{\text{s}}^2} - 1} \right)}^2}}}$$ D. $$\frac{{1 + {{\text{s}}^2}}}{{1 - {{\text{s}}^2}}}$$
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