Verify the identity:

Question

sin^(1/2)x*cosx - sin^(5/2)*cosx = cos^3x sq root sin x

I honestly have no clue how to approach the sin^(5/2)*cosx part of the equation

Answer 1

since 5/2 = 2 + 1/2, you have
u^5/2 = u^2 * u^1/2, and so,

√sinx cosx - sin^2x √sinx cosx
√sinx cosx (1-sin^2 x)
√sinx cosx cos^2x
√sinx cos^3x