Question

For \(x\in\mathbb R\), \(\cot^{-1}x=\ \ ?\)

• A. \(\dfrac{\pi}{2}-\sin^{-1}x\)
• B. \(\dfrac{\pi}{2}-\cos^{-1}x\)
• C. \(\dfrac{\pi}{2}-\tan^{-1}x\)
• D. \(\dfrac{\pi}{2}-\sec^{-1}x\)

Hint:

$\tan$ and $\cot$ are complementary: swap with $\frac{\pi}{2}-\,$angle.

Answer 1

The Correct Option is C

\(\cot\theta=\tan\!\left(\tfrac{\pi}{2}-\theta\right)\). Apply inverse on both sides (with principal ranges): \(\cot^{-1}x=\tfrac{\pi}{2}-\tan^{-1}x\).