Tg(a+b)=(tga+tgb)/(1-tgatgb);tg(a-b)=(tga-tgb)/(1+tgatgb)
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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