Question Number 188286 by mustafazaheen last updated on 27/Feb/23
$${when}\:\:\:\:\:\:{sin}\left({x}\right)+{cos}\left({x}\right)={a} \\ $$$${find}\:\:\:\:\:\:\:\:\:{sec}\left({x}\right)+{csc}\left({x}\right)=? \\ $$
Answered by ARUNG_Brandon_MBU last updated on 27/Feb/23
$$\mathrm{sin}{x}+\mathrm{cos}{x}={a}\:\Rightarrow\mathrm{sin}{x}\mathrm{cos}{x}=\frac{{a}^{\mathrm{2}} −\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{sec}{x}+\mathrm{cosec}{x}=\frac{\mathrm{sin}{x}+\mathrm{cos}{x}}{\mathrm{sin}{x}\mathrm{cos}{x}}=\frac{\mathrm{2}{a}}{{a}^{\mathrm{2}} −\mathrm{1}} \\ $$