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If `cosec^(-1)x+cosec^(-1)y+cosec^(-1)z=-(3pi)/(2),then x/y+y/z+z/x=`A. 1B. `-3`C. 3D. `3/2` |
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Answer» We know that the minimum value of `cosec^(-1)x is -(pi)/(2)` which is attained at x=-1 `therefore cosec^(-1)+cosec^(-1)y+cosec^(-1)z=-(3pi)/(2)` `rarr cos^(-1)x+cosec^(-1)+cosec^(-1)z=(-pi)/(2)+(-pi)/(2)+(pi)/(2)` `rarr x=-1,y=-1z=-1` `therefore x/y+y/z+z/x=(-1)/(-1)+(-1)/(-1)+(-1)/(-1)=3` |
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