Different problem. This time though, I have no idea where to start.
sin^1/2 x cos x - sin^5/2 x cos x = cos^3 x [The square root of] sin x
There are very good reasons for doing the following, sport:
1. Don't bump (especially in the space of 30 minutes!!! - where's the fire??)
2. Clearly state what the question is. Otherwise it must be guessed that you want to prove an identity.
3. Learn some basic latex.
4. Don't leave things to the last minute. Then it won't be so urgent. (And then you'll probably end up living longer - without ulcers).
Left hand side $\displaystyle = \sqrt{\sin x} \cos x - \sin^2 x \sqrt{\sin x} \cos x\, ^*$
$\displaystyle = \sqrt{\sin x} \cos x (1 - \sin^2 x)$
= .......
= Right hand side.
$\displaystyle ^*\, $ $\displaystyle a^{5/2} = a^2 a^{1/2} = a^2 \sqrt{a}$