已知函数f(x)=cos(-x/2)+sin(π-x/2),x∈R 若f(a)=(2√10)/5,a∈(0,π/2),求tan(2a+π/4)

问题描述:

已知函数f(x)=cos(-x/2)+sin(π-x/2),x∈R 若f(a)=(2√10)/5,a∈(0,π/2),求tan(2a+π/4)

f(x)=cos(-x/2)+sin(π-x/2)=cos(x/2)+sin(x/2)f(a)=cos(x/2)+sin(x/2)=(2√10)/5 cos(x/2)+sin(x/2)=(2√10)/5 平方 1+sina=8/5 sina=3/5 cosa=4/5 tana=3/4tan2a=2tana/(1-tan^2a)=24/7 tan(2a+π/4)=(1+...