To find the Laplace Transform for f(t) = sin^2t, we follow these steps:
1. Trigonometric Identity
The Laplace Transform is easier to calculate if we reduce the power of the sine function using the double angle identity:
2. Applying the Transform
Using the linearity property of the Laplace Transform:
3. Standard Formulas
Using the standard Laplace Transform table:
Substitute these into the equation:
4. Simplification
Combine the fractions:
Final Result:
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