A) 0
B) 1
C) \[{{\cot }^{-1}}x+{{\cot }^{-1}}y+{{\cot }^{-1}}z\]
D) None of these
Correct Answer: A
Solution :
\[{{\cot }^{-1}}\,\frac{xy+1}{x-y}+{{\cot }^{-1}}\,\frac{yz+1}{y-z}+{{\cot }^{-1}}\frac{zx+1}{z-x}\] \[={{\cot }^{-1}}y-{{\cot }^{-1}}x+{{\cot }^{-1}}z-{{\cot }^{-1}}y\]\[+{{\cot }^{-1}}x-{{\cot }^{-1}}z=0\]. Note: Students should remember this question as a formula.
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