Question

Sin3xcos5x-sin5xcos3x=0,5

Answer 1

Sin(3x-5x)=0,5
Sin(-2x)=0,5
-2x=(-1)^k•arcsin 0,5+Пк;к€Z
-2x=(-1)^k•П/6+Пк;к€Z
Х=(-1)^(к+1)•П/12-Пк/2;к€Z

Answer 2

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

sin(a - b) = sin(a)cos(b) - cos(a)sin(b)

Let's rewrite the equation using this identity:

sin(3x - 5x) = 0.5

Simplifying further:

sin(-2x) = 0.5

Now, we need to find the values of x that satisfy this equation. Taking the arcsine (inverse sine) of both sides, we have:

-2x = arcsin(0.5)

Now, we can solve for x:

x = -(1/2) * arcsin(0.5)

Using a calculator, we can find the approximate value of arcsin(0.5) to be 30 degrees or π/6 radians. Therefore:

x = -(1/2) * (30 degrees) = -15 degrees or -(π/12) radians

So, the solution to the equation sin(3x)cos(5x) - sin(5x)cos(3x) = 0.5 is x = -15 degrees or x = -(π/12) radians.