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Question Number 39231 by LX Z last updated on 04/Jul/18

$${\left({sin}^{-1}x\right)}^2+{\left({sin}^{-1}y\right)}^2+2\left({sin}^{-1}x\right)$$$$\left({sin}^{-1}y\right)={\pi }^2,then{x}^2+y^{2}isequalto?$$

Answered by tanmay.chaudhury50@gmail.com last updated on 04/Jul/18

$$a={sin}^{-1}xb={sin}^{-1}y$$$$a^2+2ab+b^2=\prod ^2$$$$a+b=\mathrm{\Pi }$$$${sin}^{-1}x+{sin}^{-1}y=\mathrm{\Pi }$$$${sin}^{-1}x=\mathrm{\Pi }-{sin}^{-1}y$$$$a+b=\mathrm{\Pi }$$$$sina=sin(\mathrm{\Pi }-b)$$$$sina=sinb$$$$a=b$$$$a+b=\mathrm{\Pi }a=\frac{\mathrm{\Pi }}{2}b=\frac{\mathrm{\Pi }}{2}$$$${sin}^{-1}x=\frac{\mathrm{\Pi }}{2}x=1$$$${sin}^{-1}y=\frac{\mathrm{\Pi }}{2}y=1$$$$x^2+y^2=2$$$$plscheck$$$$$$

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