Question

тг(а-пи/4)-тг(а+пи/4) в виде произведения

Answer 1

(tga-tgπ/4)/(1+tga*tgπ/4)-(tga+tgπ/4)/(1-tga*tgπ/4)=
=(tga-1)/(1+tga)-(tga+1)/(1-tga)=[(-(1-tga)²-(tga+1)²]/(1-tg²a)=
=(-1+2tga-tg²a-1-2tga-tg²a)/(1-tg²a)=-2(1+tg²a)/(1-tg²a)=
=-2/cos²a:(cos²a-sin²a)/cos²a=-2/cos²a*cos²a/cos2a=-2/cos2a