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
答
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)