Question
Evaluate:
\[ \tan\left(\frac{\sin^{-1}x + \cos^{-1}x}{2}\right) \quad \text{when } x = \frac{\sqrt{3}}{2} \]
Solution
We use identity:
\[ \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \]
So,
\[ \tan\left(\frac{\sin^{-1}x + \cos^{-1}x}{2}\right) = \tan\left(\frac{\pi/2}{2}\right) \]
\[ = \tan\left(\frac{\pi}{4}\right) \]
\[ = 1 \]
Final Answer:
\[ \boxed{1} \]
Key Concept
Use the identity \( \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \) to simplify expressions quickly.