f(x)=1/(2tanx)+(sin(x/2)cos(x/2))/(2(cos(x/2))^2-1),则f(pi/8)=

问题描述:

f(x)=1/(2tanx)+(sin(x/2)cos(x/2))/(2(cos(x/2))^2-1),则f(pi/8)=

2(cos(x/2))^2-1=cosx
sin(x/2)cos(x/2))=(sinx)/2
原式=1/2tanx+1/2tanx=1/tanx=cotx
fπ/8==cotπ/8
tanπ/4=2tanπ/8/(1-tanπ/8^2)=1
tanπ/8=根号2-1
cotπ/8=根号2+1