Question

Sin5x*cos3x-cos5x*sin3x=-0,5

Answer 1

Ответ: в файле

Объяснение:

Answer 2

To solve the equation sin(5x) * cos(3x) - cos(5x) * sin(3x) = -0.5, we can use the trigonometric identity for the difference of angles:

sin(A - B) = sin(A) * cos(B) - cos(A) * sin(B).

Comparing this identity to the given equation, we can see that A = 5x and B = 3x. So we can rewrite the equation as:

sin(5x - 3x) = -0.5.

Simplifying further, we have:

sin(2x) = -0.5.

To find the solutions for this equation, we need to determine the values of x that satisfy the equation sin(2x) = -0.5.

Using the unit circle or a trigonometric table, we can determine the angles that have a sine of -0.5. The two principal solutions are -30 degrees (-π/6 radians) and 210 degrees (7π/6 radians).

However, since we are solving for x, we need to find the values of x that correspond to these angles.

For -30 degrees (-π/6 radians), we can set up the equation:

2x = -π/6 + 2πn,

where n is an integer representing the number of complete cycles around the unit circle. Solving for x, we have:

x = (-π/6 + 2πn)/2.

Similarly, for 210 degrees (7π/6 radians), we have:

2x = 7π/6 + 2πn,

which leads to:

x = (7π/6 + 2πn)/2.

These equations give us the general solutions for x that satisfy the given equation. By plugging in different integer values for n, we can find multiple solutions for x.