tan(a+π/4)=2cos2a sin(a+π/4)/cos(a+π/4)=2(cos^2a-sin^2a)√2/2(sina+cosa)/√2/2(cosa-sina)=2(cosa-sina)(cosa+sina)2(cosa-sina)^2=1(cosa-sina)^2=1/21-2sinacosa=1/2sin2a=1/2