Question

Tg(2,5 · x) - 5 ∙ x = 0

Answer 1

Ответ:

Tg(2,5 · x) - 5 ∙ x = 0

Решим это тригонометрическое уравнение:

Tg(2,5 · x) - 5 ∙ x = 0

tg(2,5x) - 5x = 0

Выделим x из tg(2,5x):

2,5x tg(2,5x) - 5x = 0

tg(2,5x)(2,5) - 5x = 0 (умножили обе стороны на 2,5)

(2,5x) - 12,5x = 0 (воспользовались свойством тангенса - tg(α)(tg(α)) = 1)

0 = -10x

x = 0

Подставим x = 0 в исходное уравнение:

Tg(2,5 ∙ 0) - 5 ∙ 0 = 0

tg(0) - 5(0) = 0 (2,5∙0 = 0, согласно определению)

Ответ:

x = 0

Пошаговое объяснение:

отметь как лучший ответ

Answer 2

To solve the equation Tg(2.5x) - 5x = 0, we can follow these steps:

Step 1: Let's simplify the equation by replacing Tg with its equivalent trigonometric function, tangent:

tan(2.5x) - 5x = 0

Step 2: Rearrange the equation to isolate the tangent term:

tan(2.5x) = 5x

Step 3: Take the inverse tangent (arctan) of both sides to eliminate the tangent:

arctan(tan(2.5x)) = arctan(5x)

Step 4: Simplify the left side by using the property arctan(tan(x)) = x:

2.5x = arctan(5x)

Step 5: Solve for x by isolating it on one side of the equation:

x = (1/2.5) * arctan(5x)

Step 6: At this point, finding an exact solution is not possible algebraically. You can use numerical methods such as iteration or approximation techniques to estimate the value of x.