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Question

If cot1x+cot1y+cot1z=π2,x,y,z>0andxy<1,thenx+y+z is also equal to

A
1x+1y+1z
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B
xyz
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C
xy+yz+zx
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D
noneofthese
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Solution

The correct option is B xyz
tan1(1x)+tan1(1y)=π2cot1(z)
tan1(x+yxy1)=tan1(z)
Taking tan on both the sides, we get
x+y=z(xy1)
x+y=xyzz
x+y+z=xyz

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