Question

The expression sin(23°)cos(7°) + cos(23º)sin(7°) is equivalent to

Answer 1

`\sin(30)`

Explanation:

Given

`\sin(23) \cos(7) + \cos(23) \sin(7)`

Required

An equivalent expression

The above is an illustration of the sine formula which states:

`\sin(A) \cos(B) + \cos(A) \sin(B) = \sin(A + B)`

In this case:

`A = 23\\ B = 7`

So:

`\sin(23) \cos(7) + \cos(23) \sin(7) = \sin(23 + 7)`

`\sin(23) \cos(7) + \cos(23) \sin(7) = \sin(30)`

Hence, an equivalent expression is:
`\sin(30)`