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Prove that: sin(B-C)cos(A-D)+sin(C-A)cos...

Prove that: `sin(B-C)cos(A-D)+sin(C-A)cos(B-D)+sin(A-B)cos(C-D)=0`

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To prove the identity \[ \sin(B-C)\cos(A-D) + \sin(C-A)\cos(B-D) + \sin(A-B)\cos(C-D) = 0, \] we will use the sine addition and subtraction formulas. ...
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