Question 1184167
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If arcsin(x) + arcsin(y) + arcsin(z) = {{{3pi/2}}} then find value of x^9 + y^9 + z^9 - (1/x.y.z)^9 where / means division and ^9 means power 9.
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<pre>
Function  arcsin()  has the range from  {{{-pi/2}}}  to  {{{pi/2}}}.


Therefore, if  arcsin(x) + arcsin(y) + arcsin(z) = {{{3pi/2}}},  then it implies

    arcsin(x) = arcsin(y) = arcsin(z) = {{{pi/2}}}.


Hence,

    x = y = z = {{{sin(pi/2)}}} = 1.


Therefore,

    x^9 + y^9 + z^9 - {{{1/((x*y*z)^9)}}} = 1 + 1 + 1 - 1 = 2.


<U>ANSWER</U>.  If  arcsin(x) + arcsin(y) + arcsin(z) = {{{3pi/2}}}  then  x^9 + y^9 + z^9 - {{{1/(x*y*z)^9}}} = 2.
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Solved.