Find the Principal Value of tan-1(cos π/2)
Solution:
Given:
\[ y = \tan^{-1}(\cos \tfrac{\pi}{2}) \]
Step 1: Evaluate cos(π/2)
\[ \cos \tfrac{\pi}{2} = 0 \]
So,
\[ y = \tan^{-1}(0) \]
Step 2: Use principal value
We know:
\[ \tan^{-1}(0) = 0 \]
(Principal value range of tan-1(x) is \((- \pi/2, \pi/2)\))
Final Answer:
Principal Value = \[ 0 \]