Question

Sin65×cos110-cos65×sin110cos 170×cos10-sin170×sin10​

Answer 1

Ответ:

решение на фотографии

Answer 2

To simplify the expression sin(65) × cos(110) - cos(65) × sin(110) cos(170) × cos(10) - sin(170) × sin(10), you can use trigonometric identities.

First, you can rewrite it as:

sin(65) × cos(110) - cos(65) × sin(110) - cos(170) × cos(10) × sin(10) - sin(170) × sin(10)

Now, let's use some trigonometric identities:

1. sin(180 - x) = sin(x)
2. cos(180 - x) = -cos(x)

Using these identities:

sin(65) × cos(110) - cos(65) × sin(110) = sin(65) × cos(70) - cos(65) × sin(70) = sin(65) × sin(20) - cos(65) × cos(20)

Now, let's use the product-to-sum identities:

sin(a) × sin(b) - cos(a) × cos(b) = -cos(a + b)

So:

sin(65) × sin(20) - cos(65) × cos(20) = -cos(65 + 20)

Now we have:

-cos(85)

So, the simplified expression is -cos(85).