Question

Which sum or difference identity could be used to prove that cos(270°-theta)=-sin theta is an identity?

Answer 1

Your answer would be B.

Explanation:

Answer 2

For this case we have that by definition:

`cosine (a-b) = Cosine (a) * cosine (b) + sine (a) * sine (b)`

If we want to solve
`cosine (270-theta)`then:

`cosine (270-theta) =\\cosine (270) * cosine (theta) + sine (270) * sine (theta) =`

We know that:

`cosine (270) = 0\\sine (270) = - 1`

Substituting:

`cosine (270) * cosine (theta) + sine (270) * sine (theta) =\\0 + (- 1 * sine (theta)) =\\-sine (theta)`

Answer:

`cosine (a-b) = Cosine (a) * cosine (b) + sine (a) * sine (b)`