Inverse Trigonometric Functions Question 224
Question: If $ {{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi $ , then $ x+y+z $ is equal to
[Kerala (Engg.) 2002]
Options:
A) xyz
B) 0
C) 1
D) 2xyz
Show Answer
Answer:
Correct Answer: A
Solution:
$ {{\tan }^{-1}}x+{{\tan }^{-1}}y+{{\tan }^{-1}}z=\pi $
Therefore $ {{\tan }^{-1}}[ \frac{x+y+z-xyz}{1-xy-yz-zx} ]=\pi $
Therefore $ x+y+z-xyz=0 $
Therefore $ x+y+z=xyz $ .
BETA
