25.12.
tg(a-π/4)=3
(tga-tgπ/4) tga-1
--------------- = 3 ----------= 3
1+tgatgπ/4 1+tga
3(1+tga)=tg-1 => 3+3tga=tga-1 => 2tga=-4 => tga=-2
25.14
tg(a-π/4) - ?
sina=12/13
cosa=-√1-(12/13)²=-√25/169=-5/13 (знак минус, т.к. 3 четверть)
tga=12/13 ÷ (-5/13) = -2,4
tga-tgπ/4 -2,4-1 -3,4 17
tg(a-π/4)= ---------------- = ----------- = ------ = ----
1+tgatgπ/4 1-2,4 -1,4 7
25.18
√3-tgx
----------- = 1
1+√3tgx
tgπ/3-tgx
-------------- = 1
1+tgπ/3tgx
tg(π/3-x) = 1
π/3-x = π/4 + πn, n∈Z
-x=-π/12 + πn, n∈Z
x=π/12-πn, n∈Z
Ответ: 13π/12, π/12, -11π/12