How do you find the exact value of #sin(pi/3)cos(pi/7) - cos(pi/3)sin(pi/7)#?

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Answer 1 · 2016-06-24T03:31:08

#sin((4pi)/21)#

Notice that this fits the form of the sine subtraction formula:

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

Here, we see that

#sin(pi/3-pi/7)=sin(pi/3)cos(pi/7)-cos(pi/3)sin(pi/7)#

So, the entire expression equals:

#sin(pi/3-pi/7)=sin((4pi)/21)#

This is a more exact form of what was given, although it is still equivalent.