Verify the identity.

`sin^(1/2)(x)cos(x)-sin^(5/2)(x)cos(x)=cos^3(x)sqrt(sin(x))`

Factor out the GCF `sin^(1/2)(x)cos(x).`

`sin^(1/2)(x)cos(x)[1-sin^2(x)]=cos^3(x)sqrt(sin(x))`

Use the pythagorean identity `sin^2(x)+cos^2(x)=1.`

From this identity `1-sin^2(x)=cos^2(x).`

`sin^(1/2)(x)cos(x)[cos^2(x)]=cos^3(x)sqrt(sin(x))`

`(sin(x))^(1/2)cos^3(x)=cos^3(x)sqrt(sin(x))`

`cos^3(x)sqrt(sin(x))=cos^3(x)sqrt(sin(x))`

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