Question

Sin²альфа-tgальфа×ctgальфа​

Answer 1

Ответ:

Объяснение:

sin² а - tg а ×ctg а​=sin² а - 1 = -cos^2 a

Answer 2

The expression you provided is a combination of trigonometric functions involving the angle α. Let's break it down step by step:

1. sin²(α) means the sine of α raised to the power of 2.
2. tg(α) represents the tangent of α.
3. ctg(α) represents the cotangent of α.

So, the expression sin²(α) - tg(α) × ctg(α) can be simplified as follows:

sin²(α) - tg(α) × ctg(α) = sin²(α) - (sin(α) / cos(α)) × (cos(α) / sin(α))

Now, we can use trigonometric identities to simplify further:

1. sin²(α) = 1 - cos²(α) (using the Pythagorean identity for sine)
2. tg(α) = sin(α) / cos(α)
3. ctg(α) = cos(α) / sin(α)

So, we can rewrite the expression as:

1 - cos²(α) - (sin(α) / cos(α)) × (cos(α) / sin(α))

Now, let's simplify it step by step:

1. 1 - cos²(α) - (sin(α) / cos(α)) × (cos(α) / sin(α))
2. 1 - cos²(α) - (sin(α) × cos(α)) / (cos(α) × sin(α))

Now, notice that sin(α) × cos(α) and cos(α) × sin(α) are the same, so they cancel each other out:

1 - cos²(α) - 1

Finally, subtract 1 from 1 to get the simplified result:

0 - cos²(α)

So, the simplified expression is -cos²(α).