Question

Помогите пожалуйста!!!a) cos2x-0,5=0б) sinx*cosx=cosxСпасибо заранее.

Answer 1

А) cos2x=1/2
  2x = +-П/3+пк
x=+-п/6+пк/2
б)sinxcosx-cosx =0
cosx(sinx-1)=0
cosx=0 или sinx-1=0
x=п/2+пк     sin x =1
                    x=п/2+2пк

Answer 2

Solving the equation cos(2x) - 0.5 = 0

To solve the equation cos(2x) - 0.5 = 0, we can follow these steps:

Step 1: Add 0.5 to both sides of the equation to isolate the cosine term: cos(2x) = 0.5

Step 2: Take the inverse cosine (also known as arccos) of both sides to eliminate the cosine function: 2x = arccos(0.5)

Step 3: Solve for x by dividing both sides by 2: x = (1/2) * arccos(0.5)

The value of x can be found by evaluating the expression (1/2) * arccos(0.5). Let's calculate it.

Using a calculator or a math software, we find that arccos(0.5) is approximately 60 degrees or π/3 radians. Therefore, x is:

x ≈ (1/2) * 60° = 30°

So, the solution to the equation cos(2x) - 0.5 = 0 is x ≈ 30°.

Solving the equation sin(x) * cos(x) = cos(x)

To solve the equation sin(x) * cos(x) = cos(x), we can follow these steps:

Step 1: Subtract cos(x) from both sides of the equation to isolate the sine term: sin(x) * cos(x) - cos(x) = 0

Step 2: Factor out cos(x) from the left side of the equation: cos(x) * (sin(x) - 1) = 0

Step 3: Set each factor equal to zero and solve for x: cos(x) = 0 or sin(x) - 1 = 0

For cos(x) = 0, we know that cosine is equal to zero at 90 degrees or π/2 radians and 270 degrees or 3π/2 radians. So, we have two possible solutions for x: x = 90° and x = 270°.

For sin(x) - 1 = 0, we can add 1 to both sides of the equation to isolate the sine term: sin(x) = 1

We know that sine is equal to one at 90 degrees or π/2 radians. So, we have another possible solution for x: x = 90°.

Therefore, the solutions to the equation sin(x) * cos(x) = cos(x) are x = 90°, x = 270°, and x = 90°.

I hope this helps! Let me know if you have any further questions.