Inverse Trigonometric Functions Question 209
Question: $ {{\cot }^{-1}}\frac{xy+1}{x-y}+{{\cot }^{-1}}\frac{yz+1}{y-z}+{{\cot }^{-1}}\frac{zx+1}{z-x}= $
Options:
A) 0
B) 1
C) $ {{\cot }^{-1}}x+{{\cot }^{-1}}y+{{\cot }^{-1}}z $
D) None of these
Show Answer
Answer:
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.
BETA
