Question 119
Suppose $t$ is a real number and $\sin(2t) \gt 0$. Prove that
$$
1 + 6 \sin t \cos t \geq (\sin^3 t + \cos^3 t)(\sin t + \cos t)^3 + 16 \sin^3 t \cos^3 t,
$$
with equality iff $\cos(2t) = 0$.
$$
1 + 6 \sin t \cos t \geq (\sin^3 t + \cos^3 t)(\sin t + \cos t)^3 + 16 \sin^3 t \cos^3 t,
$$
with equality iff $\cos(2t) = 0$.