tg(a+pi/4)-tg(a-pi/4)=2tg2a

tg(a+b)=(tga+tgb)/(1-tgatgb);tg(a-b)=(tga-tgb)/(1+tgatgb)-----------------------------tg(a+π/4)+tg(a-π/4)=(tga+tgπ/4)/(1-tgatgπ/4)+(tga-tgπ/4)/(1+tgatgπ/4)==(tga+1)/(1-tga)+(tga-1)/(1+tga)=[(tga+1)²-(tga-1)²]/[(1-tga)(1+tga)]==(1+2tga+tg²a-tg²a+2tga-1)/(1-tg²a)=4tga/(1-tg²a)=2tg2a