Question

Tga = a найдите tg(п|2+a)

Answer 1

$tga=a$

по формуле приведения:

$tg(\frac{\pi }{2}+a)=-ctga \\ \\ -\frac{1}{tga}=-\frac{1}{a}$

ответ: -1/a

Answer 2

To find the tangent of the expression tg(π | 2 + a), we first need to clarify what you mean by "|". The symbol "|" is not a standard mathematical operator in trigonometry or algebra. If you meant to use it as a division symbol, then the expression should be written as tg(π / (2 + a)). In that case, here's how you can proceed:

Let's assume θ = π / (2 + a). Now, we want to find the tangent of θ, which is given by tg(θ) or tan(θ).

In trigonometry, the tangent function is defined as:

tan(θ) = opposite side / adjacent side

Since we have θ = π / (2 + a), we can't directly apply the definition of the tangent. Instead, we can use trigonometric identities to simplify the expression. One of the well-known trigonometric identities is:

tan(π/2 - θ) = 1 / tan(θ)

Using this identity, we can rewrite our expression as follows:

tan(π / (2 + a)) = tan(π / 2 - θ)

Now, θ = π / (2 + a), so:

tan(π / (2 + a)) = tan(π / 2 - π / (2 + a))

Now, let's simplify the expression within the tangent:

tan(π / 2 - π / (2 + a)) = tan(π * (1 / 2 - 1 / (2 + a)))

Next, we can simplify the angle inside the tangent:

1 / 2 - 1 / (2 + a) = (2 + a - 2) / (2 + a) = a / (2 + a)

So, the expression becomes:

tan(π / (2 + a)) = tan(π * (a / (2 + a)))

Now, using the periodicity of the tangent function (tan(x) = tan(x + n * π), where n is any integer), we can rewrite the angle π * (a / (2 + a)) as follows:

π * (a / (2 + a)) = π * (a / (2 + a) + 2n)

Now, if we set n = -a/2, the expression becomes:

π * (a / (2 + a) + 2n) = π * (a / (2 + a) - a) = π * (a - a(2 + a)) / (2 + a)

Simplifying further:

π * (a - a(2 + a)) / (2 + a) = π * (a - 2a - a^2) / (2 + a) = π * (-a^2 - a) / (2 + a) = π * -a(a + 1) / (2 + a)

So, the final expression for tg(π | 2 + a) or tan(π | 2 + a) is:

tan(π / (2 + a)) = -π * a(a + 1) / (2 + a)