Question

6sin^2x- sin x cos x-cos^2 x=3

Answer 1

Ответ:

(ниже)

Пошаговое объяснение:

$></p> <p><em><strong>Пусть tgx = y, тогда</strong></em> </p> <p><img src=$

Найдем корни уравнения:

$y + 1 = 0 ,\\3y - 4 = 0 ;\\\\y = -1 ;\\y = \frac{4}{3} .$

Подставим tgx = y, тогда

• $tg x = - 1 ,\\x_{1} = -\frac{\pi}{4} + \pi*n ;$
• $tg x = \frac{4}{3} ,\\x_{2} = arctg\frac{4}{3} + \pi*n ;$

Answer 2

To solve the equation 6sin^2x - sin x cos x - cos^2 x = 3, we can rearrange the terms and try to factorize or simplify it. Let's break it down step by step:

1. Start with the given equation: 6sin^2x - sin x cos x - cos^2 x = 3

2. Notice that we can rewrite the equation using trigonometric identities: 6sin^2x - sin x cos x - (1 - sin^2 x) = 3 6sin^2x - sin x cos x - 1 + sin^2 x = 3

3. Combine the like terms: 7sin^2x - sin x cos x - 1 = 3

4. Move all terms to one side to form a quadratic equation: 7sin^2x - sin x cos x - 4 = 0

5. Now we have a quadratic equation in terms of sin(x). Let's substitute sin(x) with another variable, say u, to simplify it: 7u^2 - u(1 - u^2) - 4 = 0 7u^2 - u + u^3 - 4 = 0

6. Combine the like terms and rearrange the equation: u^3 + 7u^2 - u - 4 = 0

At this point, we have transformed the equation into a cubic equation in terms of u. However, solving a cubic equation generally requires advanced techniques like Cardano's formula or numerical methods. If you need a specific numerical solution, please provide more details, such as the desired range or any constraints on the solution.