Question

Sin3xcos3x+cos3xsinx>0,5

Answer 1

Ответ:

x=Пn/4

Объяснение:

Answer 2

To solve the inequality sin(3x)cos(3x) + cos(3x)sin(x) > 0.5, you can use trigonometric identities and properties.

First, notice that sin(3x)cos(3x) + cos(3x)sin(x) is equivalent to sin(4x), since sin(3x)cos(3x) can be simplified to sin(6x), and sin(6x) is equal to sin(4x) due to periodicity.

So, the inequality becomes sin(4x) > 0.5.

Now, you need to find the values of x that satisfy this inequality. To do that, consider the unit circle and where the sine function is greater than 0.5.

In the unit circle, the sine function is positive in the first and second quadrants. So, you can set up two cases:

Case 1: sin(4x) > 0.5 in the first quadrant. This means 4x is in the range (0, π/2). Divide both sides by 4: 0 < x < π/8

Case 2: sin(4x) > 0.5 in the second quadrant. This means 4x is in the range (π/2, π). Divide both sides by 4: π/8 < x < π/4

So, the solution to the inequality sin(4x) > 0.5 is: 0 < x < π/8 or π/8 < x < π/4.