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)

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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)

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)
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)

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)
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