若f(tana)=sina*cosa,求f(-1)

题目

若f(tana)=sina*cosa,求f(-1)

答案

f (tana) = sina* cos a = (1/2) 2* sina*cosa = (sin2a)/2
= tana /( 1+ tan^2a)
f( x) = x/ (1+ x^2)
f(-1) = -1/2