Sin^-1x+Sin^-1y+Sin^-1z=3(pi)/2 then find x+y+z=?

Given 

sin ^(-1) x  + sin ^(-1) y + sin ^(-1) z = 3(pie)/2  [Note sin^-1 x  can be written as sin ^(-1) x]

We know that ,

as the value of angle increases , so the value of sine of that angle increses.

Therfore, larger the value of  x in the domain of sin ^(-1) x , larger the value of sin ^(-1) x.

The max. value of sin ^ (-1) x int he principal value branch is pie/2 for which x = 1.

In given question also,

all the terms are sin ^(-1)x  = sin ^(-1)y  = sin ^(-1)z must be pie/  so as to get the overall sum as 3(pie)/2.

Therfore  x = 1,  y = 1 and z =1

Hence x + y + z = 1 + 1 + 1 = 3 

Thanks !!

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