Inverse Trigonometric Functions Question 207
Question: $ {{\tan }^{-1}}x+{{\cot }^{-1}}(x+1)= $
Options:
A) $ {{\tan }^{-1}}(x^{2}+1) $
B) $ {{\tan }^{-1}}(x^{2}+x) $
C) $ {{\tan }^{-1}}(x+1) $
D) $ {{\tan }^{-1}}(x^{2}+x+1) $
Show Answer
Answer:
Correct Answer: D
Solution:
$ {{\tan }^{-1}}x+{{\cot }^{-1}}(x+1)={{\tan }^{-1}}x+{{\tan }^{-1}}( \frac{1}{x+1} ) $
$ ={{\tan }^{-1}}[ \frac{x+\frac{1}{x+1}}{1-\frac{x}{x+1}} ]={{\tan }^{-1}}(x^{2}+x+1) $ .
BETA
