Question

3.5*. Вычислите sin(π + x)cos(п/(2) + x) – cos(2π + x)sin(3п/(2) – x).

Answer 1

Воспользуемся формулами приведения. Получим 1=cos²x+sin²x

Answer 2

To simplify the expression sin(π + x)cos(π/2 + x) - cos(2π + x)sin(3π/2 - x), we can use trigonometric identities. Here are the identities we'll need:

1. sin(π + x) = -sin(x)
2. cos(π/2 + x) = -sin(x)
3. cos(2π + x) = cos(x)
4. sin(3π/2 - x) = -cos(x)

Using these identities, the expression becomes:

-sin(x) * (-sin(x)) - cos(x) * (-cos(x))

Now, let's simplify further:

sin(x) * sin(x) - cos(x) * cos(x)

Finally, we use the Pythagorean identity sin^2(x) + cos^2(x) = 1:

1 - cos^2(x)

So, the simplified expression is 1 - cos^2(x).