Very confused on trigonometry problem

Note that $(\sin (a))^5 < 1$ and $(\cos(a))^5 < 1$.

Then, we have

$\begin{array}{rcl} (\sin(a))^7 + (\cos(a))^7 &=& (\sin(a))^2(\sin(a))^5 + (\cos(a))^2 (\cos(a))^5\\ &<& (\sin(a))^2 + (\cos(a))^2\\ &=& 1 \end{array}$

The inequality is shown.