Question

Sin160cos40-cos160sin40

Answer 1

Ответ:

= sin120

Пошаговое объяснение:

Answer 2

The expression you've provided seems to involve trigonometric identities. We can use the angle sum and difference identities to simplify it.

Let's start by using the angle difference identity for sine:

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

In your expression, we have: sin(160)cos(40) - cos(160)sin(40)

Now, let's apply the angle difference identity for cosine:

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

We can rewrite sin(160) as sin(180 - 20) and cos(160) as -cos(20):

sin(160) = sin(180 - 20) = sin(20) cos(160) = -cos(20)

Now, substitute these values back into the expression:

sin(160)cos(40) - cos(160)sin(40) = sin(20)cos(40) - (-cos(20))sin(40) = sin(20)cos(40) + cos(20)sin(40)

This looks similar to the angle sum identity for sine:

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

So, in your expression, sin(20)cos(40) + cos(20)sin(40) simplifies to sin(20 + 40):

sin(20 + 40) = sin(60)

Therefore, the simplified expression is:

sin(160)cos(40) - cos(160)sin(40) = sin(60)