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Choose the correct option.
∀ x ∈ mathbbR, cot⁻¹(-x) =
$\forall x \in \mathbb{R}$, $\cot^{-1}(-x) =$
- (a)$\pi - \cot^{-1} x$
- (b)$-\tan^{-1} x$
- (c)$-\cot^{-1} x$
- (d)$\pi + \cot^{-1} x$
Answer
Answer
Correct option: (a)
Answer: (a) $\pi - \cot^{-1} x$
The standard result is $\cot^{-1}(-x)=\pi-\cot^{-1}x$ for all $x\in\mathbb{R}$, since $\cot^{-1}$ has range $(0,\pi)$.