Question Number 19809 by CheaV last updated on 16/Aug/17
$$\mathrm{If}\:\mathrm{sin}\:\theta+\mathrm{cosec}\:\theta=\mathrm{2},\:\mathrm{then}\:\mathrm{sin}^{\mathrm{2}} \theta+\mathrm{cosec}^{\mathrm{2}} \theta \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$
Answered by ajfour last updated on 16/Aug/17
$$\left(\mathrm{sin}\:\theta+\mathrm{cosec}\:\theta\right)^{\mathrm{2}} =\mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{cosec}\:^{\mathrm{2}} \theta+\mathrm{2} \\ $$$$\Rightarrow\:\mathrm{4}=\mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{cosec}\:^{\mathrm{2}} \theta+\mathrm{2} \\ $$$$\Rightarrow\:\:\mathrm{sin}\:^{\mathrm{2}} \theta+\mathrm{cosec}\:^{\mathrm{2}} \theta=\mathrm{2}\:. \\ $$