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

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Answer 1 · 2016-10-02T21:42:26

Please read the following:

#sin(A-B)=sin(A)cos(B)-cos(A)sin(B)#

If you're interested in finding out why, you can watch this clip:

Now, this means that:

#sin(40-15)#

#=sin(40)cos(15)-cos(40)sin(15)#

#=sin(30)#

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

![https://useruploads.socratic.org/5eLIcgERQ3qlwAdbw6dE_socratic_answer_3.jpg)

And you will discover that:

#sin(30)=1/2#