Question Number 163926 by cortano1 last updated on 12/Jan/22
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\left.\begin{matrix}{\mathrm{sin}\:\theta=\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \theta}\\{\mathrm{csc}\:^{\mathrm{2}} \theta−\mathrm{tan}\:^{\mathrm{2}} \theta\:=?\:}\end{matrix}\right\} \\ $$
Answered by MJS_new last updated on 12/Jan/22
$${s}^{\mathrm{2}} =\mathrm{1}−{s} \\ $$$$\Rightarrow \\ $$$$\frac{\mathrm{1}}{{s}^{\mathrm{2}} }−\frac{{s}^{\mathrm{2}} }{\mathrm{1}−{s}^{\mathrm{2}} }=\frac{\mathrm{1}}{\mathrm{1}−{s}}−\frac{\mathrm{1}−{s}}{{s}}=\frac{{s}−\left(\mathrm{1}−{s}\right)^{\mathrm{2}} }{{s}−{s}^{\mathrm{2}} }=\frac{\mathrm{4}{s}−\mathrm{2}}{\mathrm{2}{s}−\mathrm{1}}=\mathrm{2} \\ $$
Answered by cortano1 last updated on 12/Jan/22
