Question

Вычислите: tg(x+Пи/4)-tg(x-Пи/4) ; если tgx= 1/2

Answer 1

tg(x+π/4)-tg(x-π/4)=(tgx+tgπ/4)/(1-tgx*tgπ/4)-(tgx-tgπ/4)/(1+tgx*tgπ/4)=
(0,5+1)/(1-0,5)-(1-0,5)/(1+0,5)=1,5/0,5-0,5/1,5=3-1/3=2 2/3