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Question

If tan1(x)+tan1(y)+tan1(z)=π, then 1xy+1yz+1zx=

A
0
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B
1
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C
1xyz
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D
xyz
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Solution

The correct option is B 1
tan1(x)+tan1(y)+tan1(z)=π
tan1x+tan1y=πtan1z
x+y1xy=zx+y=z+xyz
x+y+z=xyz
Dividing by xyz, we get
1yz+1xz+1xy=1.
Note: Students should remember this question as a formula.

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