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Question

If x, y, z are natural numbers such that cotāˆ’1x+cotāˆ’1y=cotāˆ’1z then the number of ordered triplets (x,y,z) that satisfy the equation is ___

A
1
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B
2
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C
Infinite solutions
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Solution

The correct option is C Infinite solutions
x =1 : y =1 is not a solution of the given equation
Suppose (x,y)(1,1)
Then 1x+1y11xy=1zx(zy)=(1+yz)=(1+yz)zy
If y=n+1:z=n then x=n2+n+1
All such numbers are solutions

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