Question

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

Answer 1

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