Statement 1: If then the value of Statement 2:
Statement 1: If $0 < x < \frac{\pi}{2}$ then the value of $\tan^{-1}(\cot x) = \frac{\pi}{2} - x$
Statement 2: $\tan^{-1}(\tan x) = x, \forall x \in R$
- aStatement 1 is true and Statement 2 is false.
- bStatement 2 is true and Statement 1 is false.
- cBoth the statements are true.
- dBoth the statements are false.
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
Correct option: a
Answer: (a) Statement 1 is true and Statement 2 is false.
For $0 < x < \pi/2$, $\cot x = \tan(\pi/2 - x)$, so $\tan^{-1}(\cot x) = \pi/2 - x$, making Statement 1 true. Statement 2 is false because $\tan^{-1}(\tan x) = x$ only holds for $x \in (-\pi/2, \pi/2)$, not for all $x \in R$.
From ISC 2026 Mathematics Paper 1, question 1(vi).