Final answer:
The expression cos(40)cos(10)+sin(40)sin(10) simplifies to cos(30) or √3/2, using the cosine of a sum identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b).
Step-by-step explanation:
The expression cos(40)cos(10)+sin(40)sin(10) is equivalent to cos(30) according to the cosine of a sum identity, which states that cos(a + b) = cos(a)cos(b) - sin(a)sin(b). Thus, if you let a = 40 and b = 10, the identity will give us cos(40 + 10) = cos(50). Since the identity has a minus sign and our expression has a plus sign, we use the equivalent identity cos(a - b) = cos(a)cos(b) + sin(a)sin(b) to find the answer. Therefore, the given expression simplifies to cos(30 degrees), which is equivalent to √3/2.
The given expression cos(40)cos(10)+sin(40)sin(10) can be simplified using the trigonometric identity:
cos(a)cos(b) + sin(a)sin(b) = cos(a-b)
By applying this identity, we can rewrite the expression as:
cos(40-10)
This simplifies to:
cos(30)
Therefore, the expression equivalent to cos(40)cos(10)+sin(40)sin(10) is cos(30).