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Question

If cot1x+cot1y+cot1z=π2, then x+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
None of these
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Solution

The correct option is B xyz
We know that cot1x+cot1y=cot1xy1y+x

cot1x+cot1y+cot1z=π2

cot1xy1y+x+cot1z=π2

cot1(xy1y+x)z1z+xy1y+x=π2

(xy1y+x)z1z+xy1y+x=cotπ2

(xy1y+x)z1z+xy1y+x=0

xyzzxyzy+x+xy1=0

xyzzxy=0

x+y+z=xyz


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