Concept:
Inverse Trigonometric functions have specific identities relating co-functions. Step 1: Understanding the Question:
We are asked to find the sum of \(\sin^{-1}x\) and \(\cos^{-1}x\) where \(x = 1/2\). Step 2: Key Formula or Approach:
There are two ways to solve this:
1. Use the standard identity: \(\sin^{-1}x + \cos^{-1}x = \frac{\pi}{2}\) for \(x \in [-1, 1]\).
2. Calculate the individual angles and add them. Step 3: Detailed Solution: Method 1 (Identity):
Since \(1/2\) is within the valid domain \([-1, 1]\), the identity applies directly:
\[ \sin^{-1}(1/2) + \cos^{-1}(1/2) = \frac{\pi}{2} \] Method 2 (Calculation):
1. \(\sin^{-1}(1/2) = 30^\circ = \frac{\pi}{6}\) (since \(\sin \frac{\pi}{6} = 1/2\)).
2. \(\cos^{-1}(1/2) = 60^\circ = \frac{\pi}{3}\) (since \(\cos \frac{\pi}{3} = 1/2\)).
3. Sum = \(\frac{\pi}{6} + \frac{\pi}{3} = \frac{\pi + 2\pi}{6} = \frac{3\pi}{6} = \frac{\pi}{2}\). Step 4: Final Answer:
The value is \(\pi/2\).