Question

Sinxcos3x+cosxsin3x=0,5

Answer 1

Ответ:

Sinxcos3x+cosxsin3x=1

sin(1x+3x)=1

sin 4x=1

4x=π/2 + 2πn, n принадлежит Z

x=п/8+пn/2,  n принадлежит Z

Пошаговое объяснение:

Вроде так

Answer 2

The equation you've provided is:

sin(x)cos(3x) + cos(x)sin(3x) = 0.5

To simplify this equation, you can use the trigonometric identity for the sine of a sum of angles:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

Applying this identity to your equation:

sin(x)cos(3x) + cos(x)sin(3x) = sin(x + 3x) = sin(4x)

So, the equation becomes:

sin(4x) = 0.5

Now, to solve for x, you need to find the angles whose sine is 0.5. One such angle is π/6 (30 degrees) since sin(π/6) = 0.5. However, sine is positive in both the first and second quadrants, so another solution would be π - π/6 = 5π/6 (150 degrees).

So, the solutions for x are:

x = π/24 + k*(π/2), where k is an integer.

This represents all the possible angles that satisfy the given equation.