Comment
Share
Q)

# Write the principal value of $$cot^{-1} \{ cot \bigg( -\frac{\pi}{4} \bigg) \}$$

Comment
A)
$\frac{3\pi}{4}$
Principal interval of cot is $$(0.\pi)$$  and $$-\frac{\pi}{4}\notin\:(0,\pi)$$
We know that cot$$-\frac{\pi}{4}=cot(\pi-\frac{\pi}{4})=cot\frac{3\pi}{4}$$
$$\Rightarrow\:cot^{-1}cot-\frac{\pi}{4}=cot^{-1}cot\frac{3\pi}{4}=\frac{3\pi}{4}$$