The principal value of ^-1[434] is:

Question

The principal value of $	an^{-1}\left[\cot\dfrac{43\pi}{4}ight]$ is:

Accepted Answer

$\cot\dfrac{43\pi}{4}=\cot\left(10\pi+\dfrac{3\pi}{4}\right)=\cot\dfrac{3\pi}{4}$ (period $\pi$).

$$\tan^{-1}\left(\cot\frac{3\pi}{4}\right)=\tan^{-1}\left(\tan\left(\frac{\pi}{2}-\frac{3\pi}{4}\right)\right)=\frac{\pi}{2}-\frac{3\pi}{4}=-\frac{\pi}{4}.$$

Solutions · 1