Question

verify sin^(1/2)xcosx-sin^(5/2)xcosx=cos^(3)xsqrt(sinx)

Answer 1

for sin^(1/2)xcosx - sin^(5/2)xcosx
factor out by take the common division,
sin^(1/2)xcosx(1-sin^2x)

Answer 2

then use identity that 1-sin^2x = cos^2x
so, sin^(1/2)xcosx(1-sin^2x)=sin^(1/2)xcosxcos^2x=sin^(1/2)xcos^3x

Answer 3

that's same like cos^3xsqrt(sinx)