Question

1 - 3 sin x*cos x + cos2 x= 0.​

Answer 1

Ответ:

Объяснение: надо разложить на множители

Answer 2

To solve the equation 1 - 3sin(x)*cos(x) + cos^2(x) = 0, we can follow these steps:

Step 1: Rewrite the equation using trigonometric identities. Step 2: Factor the equation if possible. Step 3: Solve for x.

Let's begin:

Step 1: Rewrite the equation using trigonometric identities. The equation can be rewritten as follows:

1 - 3sin(x)*cos(x) + cos^2(x) = 0

Now, use the trigonometric identity: cos^2(x) = 1 - sin^2(x)

The equation becomes:

1 - 3sin(x)*cos(x) + (1 - sin^2(x)) = 0

Step 2: Factor the equation if possible. The equation is quadratic in sin(x), so let's combine like terms:

1 - 3sin(x)*cos(x) + 1 - sin^2(x) = 0

Now, simplify further:

2 - 3sin(x)*cos(x) - sin^2(x) = 0

Step 3: Solve for x. To solve for x, we need to find the values of sin(x) that satisfy the equation. Let's factor the quadratic:

-sin^2(x) - 3sin(x)*cos(x) + 2 = 0

Now, we can use the quadratic formula to solve for sin(x):

The quadratic formula is given by:

sin(x) = [-b ± √(b^2 - 4ac)] / 2a

In our equation, a = -1, b = -3*cos(x), and c = 2.

sin(x) = [3cos(x) ± √((-3cos(x))^2 - 4*(-1)2)] / 2(-1)

sin(x) = [3cos(x) ± √(9cos^2(x) + 8)] / -2

This equation gives us two potential solutions for sin(x), which will lead to two sets of solutions for x.

Set 1: sin(x) = [3cos(x) + √(9cos^2(x) + 8)] / -2 Set 2: sin(x) = [3cos(x) - √(9cos^2(x) + 8)] / -2

To find the exact values of x, we need to use a calculator to evaluate the trigonometric functions and solve for x. Keep in mind that there might be multiple solutions for x, depending on the domain of interest.