设tanx/2=t,sinx=2t/(1+t^2),为什么有dx=2dt/(1+t^2)

Question

设tanx/2=t,sinx=2t/(1+t^2),为什么有dx=2dt/(1+t^2)

Answer 1

x=2*arctan t
∴dx/dt=2/(1+t^2)
即dx=2dt/(1+t^2)