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
1) 4*a-a^3=(2-a)*a*(a+2)
2) a*x^2+2*a*x+a= a*(x+1)^2
T=tgx dt=dx/sin²x
S(1/ctg(x))*(dx/sin^2(x))
Sdt/t=lnt+C=ln(tgx)+C