Question

Sin x -cos x = -1 сробузызыжчзчзсзаззазазаазаз

Answer 1

Ответ:

Уравнение не имеет решений.

Пошаговое объяснение:

Упростить:

sin(2x)/2 = - 1

Умножаем обе части:

sin(2x) = - 2

Поскольку sin(2x) е [-1 ; 1] уравнение не имеет решений

x e/ R ("е" зачёркнутая)

Answer 2

It seems like there might be some typing or input errors in your equation. Let's try to correct it and solve it.

The equation you've provided is: sin(x) - cos(x) = -1

To solve for x, we can use some trigonometric identities. Here's the step-by-step solution:

1. First, let's square both sides of the equation to eliminate the square root: (sin(x) - cos(x))^2 = (-1)^2

2. Expand the left side using the formula (a - b)^2 = a^2 - 2ab + b^2: sin^2(x) - 2sin(x)cos(x) + cos^2(x) = 1

3. Use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to simplify: 1 - 2sin(x)cos(x) = 1

4. Now, subtract 1 from both sides to isolate the term involving sin(x) and cos(x): -2sin(x)cos(x) = 0

5. Divide both sides by -2 to solve for sin(x)cos(x): sin(x)cos(x) = 0

Now, we have sin(x)cos(x) = 0. This equation has solutions at points where either sin(x) = 0 or cos(x) = 0, or both. Let's find the solutions for both cases:

Case 1: sin(x) = 0 This occurs when x is a multiple of π (pi): x = nπ, where n is an integer.

Case 2: cos(x) = 0 This occurs when x is an odd multiple of π/2: x = (2n + 1)(π/2), where n is an integer.

So, the solutions to the equation sin(x) - cos(x) = -1 are: x = nπ, where n is an integer. x = (2n + 1)(π/2), where n is an integer.