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.

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