InterviewSolution
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InterviewSolution
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If `x , y , z in [-1,1]`such that `sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/2,`find the value of `x^2+y^2+z^2dot`A. 1B. 3C. `(3pi^(23))/(4)`D. `3pi^(2)` |
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Answer» We know that the minimum value of `sin^(-1) x for x in[-1,1]` is `-(pi)/(2)` `therefore sin^(-1)xge-(pi)/(2)sin^(-1)yge-(pi)/(2) and sin^(-1)z ge -(pi)/(2)` for all `rarr sin^(-1)x+sin^(-1)y+sin^(-1)zge(pi)/(2)+(pi)/(2)+(pi)/(2)` ` therefore sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/(2)` `rarr sin^(-1)x=(pi)/(2)sin^(-1)y -(pi)/(2),sin^(-1)z=(pi)/(2)` `rarr x==z=-1` Hence `x^(2)+y^(2)+z^(2)=(1)^(2)+(-1)^(2)+(-1)^(2)=3` |
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