Question
Find the value of:
\[ \cos(\sin^{-1}x + \cos^{-1}x), \quad |x| \le 1 \]
Solution
We use identity:
\[ \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \quad \text{for } |x| \le 1 \]
So,
\[ \cos(\sin^{-1}x + \cos^{-1}x) = \cos\left(\frac{\pi}{2}\right) \]
\[ = 0 \]
Final Answer:
\[ \boxed{0} \]
Key Concept
Use the identity \( \sin^{-1}x + \cos^{-1}x = \frac{\pi}{2} \) directly for simplification.