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.

Answer 2

It seems like you have an expression involving trigonometric functions, but there might be some confusion with the characters you used. The trigonometric function you're likely referring to is "tan" for tangent, not "tg," and the symbol "п" appears to be a placeholder for the Greek letter "π" (pi). Assuming you want to calculate the expression:

(1 + tan^2(π/12)) / (1 - tan^2(π/12))

You can simplify this expression using trigonometric identities. The identity you'll use here is the Pythagorean identity, which states that:

tan^2(x) + 1 = sec^2(x)

Using this identity, you can rewrite the expression as follows:

(1 + tan^2(π/12)) / (1 - tan^2(π/12)) = (sec^2(π/12)) / (sec^2(π/12) - 1)

Now, let's calculate sec^2(π/12):

sec(x) = 1/cos(x)

So, sec^2(π/12) = (1/cos(π/12))^2

You can find the value of cos(π/12) using a calculator or by referring to trigonometric tables. Once you have the value of cos(π/12), you can calculate sec^2(π/12).

Finally, substitute the value of sec^2(π/12) back into the expression:

(sec^2(π/12)) / (sec^2(π/12) - 1)

Simplify the expression, and you'll have your answer.