Question

1+tg²п/12 / 1-tg²п/12

Answer 1

1+tg²α=1+(sin²α/cos²α) =(cos²α+sin²α)/cos²α=1/cos²a.

1-tg²α=1-(sin²α/cos²)=(cos²α-sin²α)/cos²α = cos(2α)/cos²α.

(1+tg²α)/(1-tg²α) = (1/cos²α)/( cos(2α)/ cos²α) = (1/cos²α)*(cos²α/cos(2α)) = 1/cos(2α).

Подставим значение α = (pi/12).

Тогда 2α = (pi/6) = 30 градусов.

cos(30°) = √3/2.

Ответ: 1/ cos(30°) = 1/(√3/2) = 2/√3 = 2√3/3 ≈ 1,154701.