NDA 2016
- Exam
- NDA
- Year
- 2016
- Subject
- Mathematics
- Chapter
- Inverse Trigonometric Functions
NDA 2016 · Mathematics · Inverse Trigonometric Functions
Consider the following statements: 1. ^ -1 x+ ^ -1 ((1)/(x))=π 2....
Consider the following statements:
1. x, y \in[-1,1]x \neq y
Which of the above statements is/are correct?
Options
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Correct answer
D. Neither 1 nor 2
Step-by-step solution
Statement-1
\begin{aligned}
& \because\left(\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1} \frac{x+y}{1-x y}\right) \\
& \begin{aligned}
\tan ^{-1} x+\tan ^{-1} \frac{1}{x} & =\tan ^{-1} \frac{x+\frac{1}{x}}{1-x \cdot \frac{1}{x}} \\
& =\tan ^{-1} \frac{x^2+1}{0} \\
& =\tan ^{-1} \infty=\tan ^{-1} \tan \frac{\pi}{2}
\end{aligned}
\end{aligned}\tan ^{-1} x+\tan ^{-1} \frac{1}{x}=\frac{\pi}{2}\sin ^{-1} x+\cos ^{-1} y=\frac{\pi}{2} \quad(x, y) \in(-1,1)x=yx \neq y$.
Statement (2) is also wrong.