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Question Number 30476 by abdo imad last updated on 22/Feb/18

$$findL\left({cos}^{2}x\right)andL\left({sin}^{2}x\right)Lislaplacetransform.$$

Answered by sma3l2996 last updated on 24/Feb/18

$$L\left({cos}^{2}x\right)=L\left(\frac{cos\left(2x\right)+1}{2}\right)=\frac{1}{2}(L\left(cos\left(2x\right)\right)+L\left(1\right))$$$$=\frac{1}{2}(\frac{s}{s^2+2^2}+\frac{1}{s})$$$$samethingforL\left({sin}^2\left(x\right)\right)=\frac{1}{2}(\frac{1}{s}-\frac{2}{s^2+2^2})$$

Commented by sma3l2996 last updated on 24/Feb/18

$$L\left({sin}^2\left(x\right)\right)=\frac{1}{2}(\frac{1}{s}-\frac{s}{s^2+2^2})$$

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