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

(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