Question

Sin40×cos10-sin10cos40​

Answer 1

Ответ:

Объяснение:

$\[\sin40\cdot \cos10-\sin10\cdot \cos40=\sin(40-10)=\sin30=\boxed{\frac{1}{2}}\]$

Для решения использовали формулу:

$\[\sin(\alpha \pm\beta)=\sin\alpha\cos\beta \pm \sin\beta\cos\alpha\]$

Answer 2

Ответ: sin30

Объяснение:

Answer 3

To solve the trigonometric expression sin(40) × cos(10) - sin(10) × cos(40), you can use trigonometric identities. Specifically, the product-to-sum identity for sine and cosine is helpful in this case:

sin(A) × cos(B) - sin(B) × cos(A) = sin(A - B)

Using this identity, we have:

sin(40) × cos(10) - sin(10) × cos(40) = sin(40 - 10) = sin(30)

Now, we need to find the value of sin(30). The sine of 30 degrees is a well-known value:

sin(30°) = 0.5

So, the final result of the expression is:

sin(40) × cos(10) - sin(10) × cos(40) = sin(30) = 0.5