`sin^(1/2)x cosx - sin^(5/2)x cosx = cos^3(x)sqrt(sin(x))` Verify the identity.

Expert Answers
mathace eNotes educator| Certified Educator

Verify the identity.


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


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

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




scisser | Student

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

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

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

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