سلسلة المعادلات

$Q19)solve .in.R$

$ tanx+tany=1$

$x+y=\frac{\pi }{4}$


$Q20)solve.in.[0,2\pi ]$

$sinx+siny=1$

$cos2x-cos2y=1$

$\large {\color{Red} x+y=\frac{\pi}{4}\Rightarrow \tan(x+y)=1\Rightarrow 1-tanxtany=1}$
$\large {\color{Red} \tan(x)\tan(y)=0\Rightarrow x=n\pi ,,OR,, y=n\pi}$
\$\large {\color{Red} \rightarrow y=(\pi/4)-n\pi,,OR,,x=(\pi/4)-n\pi}$

$\large {\color{Red} cos2x-cos2y=1\Rightarrow 1-2sin^{2}x-1+2sin^{2}y=1}$
${\color{Red} \Rightarrow 2(sin^{2}y-sin^{2}x)=1\rightarrow (siny-sinx)(siny+sinx)=1/2} $
${\color{Red} \Rightarrow sinx+siny=1,,siny-sinx=1/2\Rightarrow siny=3/4,,sinx=1/4}$
$ {\color{Red} \Rightarrow x=0.24,,x=\pi-0.24,,y=0,88,,y=\pi-0.88}$

$Q21)solve.in.[0,2\pi ]$

$sinx+cosy=1$

$cos2x-cos2y=1$

للتذكير ؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟؟

$Q22)1+\left | log_4{(9x^{2}-39x+43)} \right |=\left | cos((x-2)cosx) \right |$

$Q23)solve in [0,\pi ]$

$sin^{8}x+cos^{8}x-cos^{2}2x=0$

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