Question Number 73817 by Rio Michael last updated on 16/Nov/19
$${find}\:{the}\:{solutions}\:{of}\:{the}\:{equation} \\ $$$${in}\:\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\:\pi \\ $$$$\:\:{sin}\mathrm{2}\theta\:=\:{sec}\theta \\ $$
Answered by mr W last updated on 16/Nov/19
$$\mathrm{sin}\:\mathrm{2}\theta\leqslant\mathrm{1} \\ $$$$\mathrm{sec}\:\theta\geqslant\mathrm{1} \\ $$$$\mathrm{sin}\:\mathrm{2}\theta=\mathrm{1}\:\Rightarrow\theta=\frac{\pi}{\mathrm{4}} \\ $$$$\mathrm{sec}\:\theta=\mathrm{1}\:\Rightarrow\theta=\mathrm{0} \\ $$$$\Rightarrow{no}\:{solution}\:{for}\:\theta\:{such}\:{that}\:\mathrm{sin}\:\mathrm{2}\theta=\mathrm{1}\:{and}\:\mathrm{sec}\:\theta=\mathrm{1}! \\ $$
Commented by Rio Michael last updated on 16/Nov/19
$${thanks} \\ $$
Commented by peter frank last updated on 16/Nov/19
$${thank}\:{you} \\ $$