N=tan(pai/8)*[tan(pai/8)+2)化简

1=tan(π/4)=2tan(π/8)/[1-tan^(π/8)]

--->2tan(π/8)=1-tan^(π/8)

--->2tan(π/8)+tan^(π/8)=1

--->N=tan(π/8)[tan(π/8)+2]=1

N=tan(pai/8)*[tan(pai/8)+2)化简

N=tan(π/8)×[tan(π/8)+2]

=[(1-cosπ/8)/sinπ/8]×[(1-cosπ/8)/sinπ/8+2]

= (1-√2/2)/√2/2×[(1-√2/2)/√2/2+2]

=(√2-1)×(√2+1)

=2-1

=1