Question
One of the below will equal cos(360∘+x).sin(x−360∘)
Answers
GPT 3.5
Let's use the sum and difference identities for cosine and sine to simplify the expression:
cos(360∘+x).sin(x−360∘)
= cos(360∘)cos(x)sin(x) - sin(360∘)sin(x)
= (cos(360∘)cos(x)sin(x) - cos(360∘)sin(x)cos(x))
Since cos(360∘) = 1 and sin(360∘) = 0, this simplifies to:
= cos(x)sin(x) - 0
= sin(x)cos(x)
Therefore, cos(360∘+x).sin(x−360∘) is equal to sin(x)cos(x).
cos(360∘+x).sin(x−360∘)
= cos(360∘)cos(x)sin(x) - sin(360∘)sin(x)
= (cos(360∘)cos(x)sin(x) - cos(360∘)sin(x)cos(x))
Since cos(360∘) = 1 and sin(360∘) = 0, this simplifies to:
= cos(x)sin(x) - 0
= sin(x)cos(x)
Therefore, cos(360∘+x).sin(x−360∘) is equal to sin(x)cos(x).