Question Number 45829 by jashim last updated on 17/Oct/18
$$\mathrm{Given}\:{A}=\:\mathrm{sin}^{\mathrm{2}} \theta\:+\:\mathrm{cos}^{\mathrm{4}} \theta,\:\mathrm{then}\:\mathrm{for}\:\mathrm{all} \\ $$$$\mathrm{real}\:\theta \\ $$
Commented by MJS last updated on 17/Oct/18
$$\mathrm{this}\:\mathrm{isn}'\mathrm{t}\:\mathrm{a}\:\mathrm{clear}\:\mathrm{question}. \\ $$$$\mathrm{another}\:\mathrm{possible}\:\mathrm{answer}\:\mathrm{is} \\ $$$${A}=\mathrm{sin}^{\mathrm{2}} \:\theta\:+\mathrm{cos}^{\mathrm{4}} \:\theta\:\wedge\:\theta\in\mathbb{R}\:\Rightarrow\:{A}\geqslant\mathrm{0} \\ $$
Commented by MJS last updated on 17/Oct/18
$${A}=\frac{\mathrm{7}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{8}}\mathrm{cos}\:\mathrm{4}\theta \\ $$