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Study the Assertion and Reason and choose the correct option.
The equality tan(cot⁻¹ x) = cot(tan⁻¹ x), is true for all x ∈ R
Assertion: The equality $\tan(\cot^{-1} x) = \cot(\tan^{-1} x)$, is true for all $x \in R$
Reason: The identity $\tan^{-1} x + \cot^{-1} x = \frac{\pi}{2}$, is true for all $x \in R$ Which of the following is correct? (Application)
- (a)Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
- (b)Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
- (c)Assertion is true and Reason is false.
- (d)Assertion is false and Reason is true.
Answer
Answer
Official answer keyCorrect option: (a)
Answer: (a) Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
Using $\tan^{-1}x + \cot^{-1}x = \frac{\pi}{2}$: $\cot^{-1}x = \frac{\pi}{2} - \tan^{-1}x$, so $\tan(\cot^{-1}x) = \cot(\tan^{-1}x)$ (the official key takes this as true for all $x$).