Find the Principal Value of cot-1(tan 3π/4)
Solution:
Step 1: Evaluate tan(3π/4)
\[ \tan \frac{3\pi}{4} = -1 \]
So,
\[ y = \cot^{-1}(-1) \]
Step 2: Use known value
\[ \cot\left(\frac{3\pi}{4}\right) = -1 \]
Principal value range of cot⁻¹(x):
\[ (0, \pi) \]
Since \( \frac{3\pi}{4} \in (0,\pi) \),
\[ y = \frac{3\pi}{4} \]
Final Answer:
Principal Value = \[ \frac{3\pi}{4} \]