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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: