How can we express sin(57)cos(13) + cos(57)sin(13) in terms of sine or cosine?

The expression sin(57)cos(13) + cos(57)sin(13) can be simplified using the sine addition formula.

According to the sine addition formula, we know that:

sin(a + b) = sin(a)cos(b) + cos(a)sin(b)

In this case, we can let a = 57 and b = 13. So, applying the formula:

sin(57 + 13) = sin(57)cos(13) + cos(57)sin(13)

Therefore, the expression simplifies to sin(70).

To summarize, sin(57)cos(13) + cos(57)sin(13) = sin(70), showing how we can represent the given expression as the sine of an angle.

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