化简 cos(2tan-1x) tan-1x 指的是 tanx的反函数

问题描述:

化简 cos(2tan-1x) tan-1x 指的是 tanx的反函数

设 tanα = x,则 tan-1x = α
并且,tan(2α) = 2tanα / (1 - tan²α)
sec²α = 1 / cos²α = 1 + tan²α
  cos(2tan-1x)
  = cos(2α)
  = cos²α - sin²α
  = cos²α (1 - tan²α)
  = (1 - tan²α) / (1 + tan²α)
  = (1 - x²) / (1 + x²)