lim(x→π/4) tan2x*tan(π/4-x)=lim(x→π/4) 2tanx/(1-tan^2x)*[tan(π/4)-tan(x)]/[1+tan(π/4)*tan(x)]=lim(x→π/4) 2tanx/(1-tan^2x)*[1-tan(x)]/[1+tan(x)]=lim(x→π/4) 2tanx/(1+tanx)^2=1/2