Show that $\sin^5 x + \cos^3 x \geq \sin^3 x + \cos^2 x$ implies the expression equals $1$, and find when equality holds.
$\sin^5 x + \cos^3 x \geq \sin^3 x + \cos^2 x = 1$ Equality holds only when: $\sin^5 x = \sin^2 x \Rightarrow \sin^3 x = 1$ and $\cos^3 x = \cos x \Rightarrow \cos x = 1$.
Show that $\sin^5 x + \cos^3 x \geq \sin^3 x + \cos^2 x$ implies the expression equals $1$, and find when equality holds.