Question

Получается что-то не понятное) помогите пожалуйста) 2 tgx - 3 ctg x +1 = 0

Answer 1

Ctg это 1/ на tg, заменили вначале его, потом ввели новую переменную и начали решать обычное квадратное уравнение , после того как нашли корни ввели обратную замену))) удачи

Answer 2

Solving the Equation 2tg(x) - 3ctg(x) + 1 = 0

To solve the equation 2tg(x) - 3ctg(x) + 1 = 0, we can use trigonometric identities and properties to simplify and solve for the value of x.

Solution:

Using the identity that cotangent (ctg) is the reciprocal of tangent (tg), we can rewrite the equation in terms of tangent:

2tg(x) - 3 * (1/tg(x)) + 1 = 0

Now, let's simplify the equation further:

2tg(x) - 3/tg(x) + 1 = 0

To simplify the equation, we can multiply through by tg(x) to clear the fraction:

2tg^2(x) - 3 + tg(x) = 0

This gives us a quadratic equation in terms of tangent. We can now solve for tg(x) using the quadratic formula:

tg(x) = (-b ± √(b^2 - 4ac)) / (2a)

Where a = 2, b = 1, and c = -3.

Plugging these values into the quadratic formula, we can find the solutions for tg(x).

Conclusion:

By solving the quadratic equation for tg(x), we can find the values of x that satisfy the original equation 2tg(x) - 3ctg(x) + 1 = 0.