Question Number 57448 by Pk1167156@gmail.com last updated on 04/Apr/19
$$\mathrm{If}\:\:\:\mathrm{sin}\:{x}+\mathrm{cosec}\:{x}=\mathrm{2},\:\mathrm{then}\:\mathrm{sin}^{{n}} {x}+\mathrm{cosec}^{{n}} {x} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$
Answered by tanmay.chaudhury50@gmail.com last updated on 04/Apr/19
$${a}+\frac{\mathrm{1}}{{a}}=\mathrm{2} \\ $$$${a}^{\mathrm{2}} +\mathrm{1}=\mathrm{2}{a} \\ $$$$\left({a}−\mathrm{1}\right)^{\mathrm{2}} =\mathrm{0}\:\:{so}\:{a}=\mathrm{1} \\ $$$${sinx}={a}=\mathrm{1} \\ $$$${cosecx}=\frac{\mathrm{1}}{{a}}=\mathrm{1} \\ $$$${sin}^{{n}} {x}+{cosec}^{{n}} {x} \\ $$$$\left(\mathrm{1}\right)^{{n}} +\left(\mathrm{1}\right)^{{n}} \\ $$$$=\mathrm{2} \\ $$