Question Number 189916 by mustafazaheen last updated on 24/Mar/23
$$\mathrm{when}\:\:\:\:\mathrm{sinx}×\mathrm{cosx}=−\frac{\mathrm{1}}{\mathrm{4}} \\ $$$$\mathrm{find}\:\:\:\:\:\:\:\mathrm{sinx}+\mathrm{cosx}=? \\ $$
Answered by aminitindas last updated on 24/Mar/23
$$ \\ $$$$\boldsymbol{\mathrm{Ans}}: \\ $$$$\left(\mathrm{sin}{x}\:+\:\mathrm{cos}{x}\right)^{\mathrm{2}} \:=\:\mathrm{sin}^{\mathrm{2}} {x}\:+\:\mathrm{cos}^{\mathrm{2}} {x}\:+\:\mathrm{2sin}{x}\mathrm{cos}{x} \\ $$$$\left(\mathrm{sin}{x}\:+\:\mathrm{cos}{x}\right)^{\mathrm{2}} \:=\:\mathrm{1}+\:\mathrm{2}\left(−\frac{\mathrm{1}}{\mathrm{4}}\right)=\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{sin}{x}\:+\:\mathrm{cos}{x}\:=\:\pm\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}} \\ $$$$ \\ $$$${aminitindas},\:\mathrm{March}\:\mathrm{24},\:'\mathrm{23} \\ $$
Answered by CElcedricjunior last updated on 26/Mar/23
$$\begin{cases}{\boldsymbol{{sinx}}×\boldsymbol{{cosx}}=−\frac{\mathrm{1}}{\mathrm{4}}}\\{\boldsymbol{{sinx}}+\boldsymbol{{cosx}}=\boldsymbol{{k}}}\end{cases} \\ $$$$\boldsymbol{{calculons}}\:\boldsymbol{{sinx}}+\boldsymbol{{cosx}}=\boldsymbol{{k}}\:\blacksquare\boldsymbol{{M}}{oivre} \\ $$$$\boldsymbol{{on}}\:\left(\boldsymbol{{cosx}}+\boldsymbol{{sinx}}\right)^{\mathrm{2}} =\mathrm{1}+\mathrm{2}\boldsymbol{{sinxcosx}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\boldsymbol{{sinx}}+\boldsymbol{{cosx}}=\mp\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\ $$$$\mathscr{L}{e}\:{mignon}\:{fofana}\:{cedric}\:{junior} \\ $$$$ \\ $$