Question

Tgx + 3 ctgx = 4плиз пж​

Answer 1

Ответ:

Объяснение:

Известно, что ctg x = 1 / tg x. В связи с этим, перепишем уравнение так:

tg x + 3 / tg x - 4 = 0

Введём замену. Пусть tg x = a, причём a ≠ 0

a + 3/a - 4 = 0

(a² + 3 - 4a) / a = 0

Из свойств дроби, равной нулю, вытекает, что

a² - 4a + 3 = 0 (1)

a ≠ 0

a² - 4a + 3 = 0

a1 = 3; a2 = 1

Данное дробно-рациональное уравнение имеет корни 3 и 1.Теперь:

tg x = 3                             или                                       tg x = 1

x = arctg 3 + πn,n∈Z                                                   x = π/4 + πk,k∈Z

Answer 2

The equation you've given appears to involve trigonometric functions. The equation is:

Tgx + 3 ctgx = 4

It seems like you might be referring to the tangent and cotangent functions. However, I'm not sure if "Tgx" and "ctgx" are typos or abbreviations for something. If you meant "tan(x)" for tangent and "cot(x)" for cotangent, then your equation would look like this:

tan(x) + 3cot(x) = 4

If you're looking for a solution to this equation in terms of x, I can guide you through the process.

First, let's simplify the equation by expressing cot(x) in terms of 1/tan(x):

tan(x) + 3 * (1/tan(x)) = 4

Now, let's clear the fraction by multiplying both sides of the equation by tan(x):

tan^2(x) + 3 = 4tan(x)

Now we have a quadratic equation in terms of tan(x):

tan^2(x) - 4tan(x) + 3 = 0

This can be factored:

(tan(x) - 1)(tan(x) - 3) = 0

So, tan(x) = 1 or tan(x) = 3.

Now, you can find the angles that satisfy these conditions using inverse tangent (arctan) functions:

For tan(x) = 1: x = arctan(1) = π/4 (45 degrees)

For tan(x) = 3: x = arctan(3)

However, finding the exact value of arctan(3) involves a non-integer value that cannot be represented exactly using common angles. It's an irrational value.

So, the solution for the equation tan(x) + 3cot(x) = 4 is approximately:

x = π/4 and x ≈ 1.249 radians (or its equivalent in degrees).

Please note that there might be some confusion due to the notation you used. If "Tgx" and "ctgx" mean something different, please clarify, and I'll be happy to assist you accordingly.