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Find x^2 + y^2+ z^2 - 4xyz if \[\sin ^{-1}x+\sin ^{-1} y+\sin ^{-1}z = \frac{ 3\Pi }{ 2 }\]?
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shubhamsrg
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7
hint :
max value of sin^-1 x ?
Fazeelayaz
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ye sawal kaha se liya hai
shubhamsrg
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arre,,arent you getting the catch ?
that was a great thing acc to me,,whats the max value of xin^-1 x? o.O
shubhamsrg
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great hint* :P
Fazeelayaz
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u mean max value of sinx-1 or sinx
shubhamsrg
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sin^-1
shubhamsrg
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inverse
Fazeelayaz
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pi/2 + pi/2 +pi/2 do u mean that
shubhamsrg
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yep..the only possible ans..
Fazeelayaz
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hmm i don't think so
shubhamsrg
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really,,what makes you argue ?
Fazeelayaz
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try that formula sin-1x + sin-1y=sin-1(x(1-y^2)^1/2+y(1-x^2)^1/2)
Fazeelayaz
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bring sins into one form like sin-1(.....)=3pi/2
Fazeelayaz
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ok u are may be right
Fazeelayaz
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i was just trying to confirm it
shubhamsrg
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ofcorse am right,,
suppose i ask you sinx +siny + sinz =3, then ofcorse its possible when all are =1
shubhamsrg
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same with this case..
hence x=y=z =1
Yahoo!
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@shubhamsrg Why Did u Take sin as Maximum ? Sorry My Connection was Out Of Order :)
Yahoo!
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@satellite73 @RadEn
anonymous
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@shubhamsrg provided you with the answer
mukushla
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i go with @shubhamsrg\[\sin ^{-1}x+\sin ^{-1} y+\sin ^{-1}z \le \frac{ 3\pi }{ 2 }\]equality occurs when\[\sin ^{-1}x=\sin ^{-1} y=\sin ^{-1}z = \frac{\pi }{ 2 }\]
anonymous
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you have
\[\sin^{-1}(x)+\sin^{-1}(y)+\sin^{-1}(z)=\frac{3\pi}{2}\] but the the very largest \(\sin^{-1}(x)\) can be is \(\frac{\pi}{2}\) so they must each be \(\frac{\pi}{2}\), otherwise they cannot add to \(\frac{3\pi}{2}\)