Multiple choice general knowledge math & puzzles

If y = tan^-1 [Ö1 - cos x/1 + cos x] then d^2y/dx^2 is

  1. 1/2

  2. 1/cos x

  3. 0

  4. 1

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The expression simplifies using trigonometric identities: (1-cos x)/(1+cos x) = tan^2(x/2). Thus, y = tan^-1(tan(x/2)) = x/2. The first derivative dy/dx is 1/2, and the second derivative d^2y/dx^2 is 0. The stored answer correctly identifies the second derivative.