Find the least value of 16 se$c^2$θ + 9 co$s^2$θ.

Put $t$ = se$c^2$θ ≥ 1: $f(t)=16t+9/t$. AM–GM would give 24 at $t=3/4$, but $t$ cannot be below 1. $f$ increases for $t$ ≥ 3/4, so the least value is at $t=1:16+9=25$.