Find the value of cos-1 (-1/2) + 2 sin-1 (1/2) ?

To solve this problem, we need to find the values of cos^-1 (-1/2) and sin^-1 (1/2) separately, and then add them together.

Step 1: Find the value of cos^-1 (-1/2) The value of cos^-1 (-1/2) is the angle whose cosine is -1/2. This angle is 120 degrees or 2π/3 radians.

Step 2: Find the value of sin^-1 (1/2) The value of sin^-1 (1/2) is the angle whose sine is 1/2. This angle is 30 degrees or π/6 radians.

Step 3: Add the two values together We have 2 sin^-1 (1/2), so we multiply the value of sin^-1 (1/2) by 2. This gives us 2 * 30 degrees = 60 degrees or 2 * π/6 radians = π/3 radians.

Finally, we add the two values together: 120 degrees + 60 degrees = 180 degrees or 2π/3 radians + π/3 radians = π radians.

So, cos^-1 (-1/2) + 2 sin^-1 (1/2) = 180 degrees or π radians.