Question

Sinα*cosα-? sinα+cosα=0.2

Answer 1

Ответ:

-0,48

Пошаговое объяснение:

(sinα+cosα)^2=(0.2)^2

sin^2α+2sinαcosα+cos^2α=0.04

1+2sinαcosα=0.04

2sinαcosα=0,04-1

2sinαcosα=-0,96

sinαcosα=-0,96/2

sinαcosα=-0,48

Answer 2

To solve the equation sin(α) * cos(α) - sin(α) + cos(α) = 0.2, we can use some trigonometric identities and algebraic manipulation.

Let's factor out sin(α) and cos(α):

sin(α) * cos(α) - sin(α) + cos(α) = 0.2

sin(α) * cos(α) - (sin(α) - cos(α)) = 0.2

Now, we can use the Pythagorean identity for sine and cosine:

sin²(α) + cos²(α) = 1

Rearrange it:

sin²(α) = 1 - cos²(α)

Now, substitute this into the equation:

(sin²(α) - cos²(α)) - (sin(α) - cos(α)) = 0.2

Now, let's make a substitution to simplify further. Let y = cos(α):

(sin²(α) - y²) - (sin(α) - y) = 0.2

Now we have a quadratic equation in terms of y:

sin²(α) - y² - sin(α) + y - 0.2 = 0

Let's solve this quadratic equation for y using the quadratic formula:

y = [-b ± √(b² - 4ac)] / (2a)

In this case, a = 1, b = -1, and c = -0.2:

y = [1 ± √((-1)² - 4(1)(-0.2))] / (2(1))

y = [1 ± √(1 + 0.8)] / 2

y = [1 ± √1.8] / 2

Now, you have two possible values for y:

1. y₁ = [1 + √1.8] / 2
2. y₂ = [1 - √1.8] / 2

Now, remember that y = cos(α). So, for each value of y, you can find the corresponding values of α:

1. For y₁ = [1 + √1.8] / 2: α₁ = arccos([1 + √1.8] / 2)

2. For y₂ = [1 - √1.8] / 2: α₂ = arccos([1 - √1.8] / 2)

These are the solutions for α that satisfy the given equation. Please note that these solutions may not be unique, as trigonometric equations often have multiple solutions over a certain interval.