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

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