How do you rewrite sin40cos15-cos40sin15 as a function of a single angle and then evaluate?

Oct 2, 2016

Explanation:

$\sin \left(A - B\right) = \sin \left(A\right) \cos \left(B\right) - \cos \left(A\right) \sin \left(B\right)$

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Now, this means that:

$\sin \left(40 - 15\right)$

$= \sin \left(40\right) \cos \left(15\right) - \cos \left(40\right) \sin \left(15\right)$

$= \sin \left(30\right)$

You can evaluate sin(30) by drawing a diagram as such:

$\sin \left(30\right) = \frac{1}{2}$