Question

Cos² x - 3 cos x = 4СРОЧНО​

Answer 1

Смотри..................

Answer 2

To solve the equation cos² x - 3 cos x = 4, we can rearrange the terms and solve for cos x.

1. Start with the equation: cos² x - 3 cos x = 4

2. Rearrange the terms to form a quadratic equation: cos² x - 3 cos x - 4 = 0

3. Let's substitute cos x with a variable, let's say y, to simplify the equation: y² - 3y - 4 = 0

4. Now, we can solve this quadratic equation by factoring or by using the quadratic formula. Let's use factoring in this case.

   The equation can be factored as (y - 4)(y + 1) = 0

   Setting each factor to zero gives us two possible solutions: y - 4 = 0 or y + 1 = 0

   Solving these equations separately, we get: y = 4 or y = -1

5. Now, we substitute y back with cos x:

   For y = 4, we have: cos x = 4

   For y = -1, we have: cos x = -1

6. However, the range of the cosine function is -1 ≤ cos x ≤ 1, so cos x cannot be equal to 4. Therefore, we discard the solution cos x = 4.

7. The valid solution is cos x = -1.

So, the solution to the equation cos² x - 3 cos x = 4 is cos x = -1.