Question

Sin⁴aльфа +2sin²aльфа ×cos²aльфа+cos⁴aльфа​

Answer 1

Ответ:

Объяснение:

(sin²α+cos²α)²=1²=1

Answer 2

The expression you've given appears to be a trigonometric expression involving sine and cosine functions. To simplify it, you can use trigonometric identities. In this case, you can use the double-angle identity for cosine:

cos(2θ) = cos²(θ) - sin²(θ)

Let's apply this identity to your expression:

sin⁴(α) + 2sin²(α) × cos²(α) + cos⁴(α)

Now, using the double-angle identity for cosine (θ = α):

= sin⁴(α) + 2(sin²(α) × (1 - sin²(α))) + cos⁴(α)

Now, distribute the 2:

= sin⁴(α) + 2sin²(α) - 2sin⁴(α) + cos⁴(α)

Combine like terms:

= -sin⁴(α) + 2sin²(α) + cos⁴(α)

Now, you can use the Pythagorean identity for sine and cosine:

sin²(α) + cos²(α) = 1

So, sin⁴(α) + cos⁴(α) = (sin²(α) + cos²(α))² - 2sin²(α)cos²(α) = 1² - 2sin²(α)cos²(α) = 1 - 2sin²(α)cos²(α)

Now, substitute this back into the expression:

= -(1 - 2sin²(α)cos²(α)) + 2sin²(α) + (1 - 2sin²(α)cos²(α))

= -1 + 2sin²(α)cos²(α) + 2sin²(α) + 1 - 2sin²(α)cos²(α)

Now, you can see that the -1 and +1 cancel out, and you're left with:

= 2sin²(α)

So, the simplified expression is 2sin²(α).