Use a sum or difference formula to find the exact value of the following. sin(pi )/(4)cos(pi )/(12)-cos(pi )/(4)sin(pi )/(12)

To find the exact value of the given expression, we can use the sine difference formula:<br /><br />$\sin(A - B) = \sin A \cos B - \cos A \sin B$<br /><br />In this case, we have:<br /><br />$\sin\frac {\pi }{4}\cos\frac {\pi }{12}-\cos\frac {\pi }{4}\sin\frac {\pi }{12}$<br /><br />Comparing this with the sine difference formula, we can see that:<br /><br />$A = \frac {\pi }{4}$ and $B = \frac {\pi }{12}$<br /><br />Substituting these values into the sine difference formula, we get:<br /><br />$\sin\left(\frac {\pi }{4} - \frac {\pi }{12}\right)$<br /><br />Simplifying the expression inside the sine function:<br /><br />$\sin\left(\frac {3\pi }{12} - \frac {\pi }{12}\right) = \sin\left(\frac {2\pi }{12}\right) = \sin\left(\frac {\pi }{6}\right)$<br /><br />We know that $\sin\left(\frac {\pi }{6}\right) = \frac {1}{2}$.<br /><br />Therefore, the exact value of the given expression is $\frac {1}{2}$.