Question

Sin(п-п/3)cos(п+п/6)tg(п/2+п/3)

Answer 1

Решение задания смотри на фотографии

Answer 2

To solve this expression, let's first simplify each trigonometric term step by step:

1. Sin(π - π/3): Using the angle subtraction formula for sine, sin(π - x) = sin(π)cos(x) - cos(π)sin(x). Here, x = π/3, so sin(π - π/3) = sin(π)cos(π/3) - cos(π)sin(π/3).

Since sin(π) = 0 and cos(π) = -1, the above expression becomes: sin(π - π/3) = 0 * cos(π/3) - (-1) * sin(π/3) = sin(π/3).

2. Cos(π + π/6): Using the angle addition formula for cosine, cos(π + x) = cos(π)cos(x) - sin(π)sin(x). Here, x = π/6, so cos(π + π/6) = cos(π)cos(π/6) - sin(π)sin(π/6).

Since cos(π) = -1 and sin(π) = 0, the above expression becomes: cos(π + π/6) = -1 * cos(π/6) - 0 * sin(π/6) = -cos(π/6).

3. Tg(π/2 + π/3): Tangent is not defined at π/2, so tg(π/2 + π/3) is undefined.

Now, combining the simplified trigonometric terms:

Sin(π - π/3)cos(π + π/6)tg(π/2 + π/3) = sin(π/3) * (-cos(π/6)) * tg(π/2 + π/3).

As mentioned above, tg(π/2 + π/3) is undefined, so the entire expression is undefined.