Write the following expression as the sine, cosine, or tangent of an angle:
cos45°cos120° - sin45°sin120°
cos(a)cos(b)-sin(a)sin(b)=cos(a+b)
Answer:cos(45+120)=cos165
To write the expression cos45°cos120° - sin45°sin120° as the sine, cosine, or tangent of an angle, we can use the trigonometric identity for the difference of two angles:
cos(A - B) = cosAcosB + sinAsinB
Let A = 45° and B = 120°. Applying the identity, we have:
cos(45° - 120°) = cos45°cos120° + sin45°sin120°
Therefore, the given expression is equal to cos(45° - 120°).