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Choose the correct option.
Statement 1: If 0 < x < π/2 then the value of tan⁻¹(cot x) = π/2 - x Statement 2: tan⁻¹(tan x) = x…
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
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 $x \in R$.