Question

已知函数f(x)=cos(-x/2)+sin(π-x/2)，x∈R

若f(a)=2根号下10/5 a∈（0，π/2)求tan(a+π/4)

Answer 1

f(x)=cos(-x/2)+sin(π-x/2)
=cosx/2+sinx/2
f(a)=cos(a/2)+sin(a/2)=（2√10）/5
cos(a/2)+sin(a/2)=（2√10）/5
平方 1+sina=8/5
sina=3/5
cosa=4/5
tana=3/4
tan（a+π/4)=(1+tana)/(1-tan^2a)=7