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

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

人气：422 ℃　时间：2020-06-03 18:00:44

解答

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