Question

Найти значение выражения tg ( п/4 - а) = 3. Найти 2tg a

Answer 1

tg(π/4-a)=(tgπ/4-tga)/(1+tgπ/4*tga)=(1-tga)/(1+tga)
(1-tga)/(1+tga)=3
1-tga=3+3tga
4tga=-2
2tga=-1

Answer 2

π/4 - α = arctg3

α = π/4 - arctg3

2tgα = 2tg(π/4 - arctg3) = 2(tg(π/4) - tg(arctg3))/(1 + tg(π/4)tg(arctg3)) = 2(1 - 3)/(1 + 1×3) = -4/(4) = -1

Ответ: -1