Prove that \[ \sin \left(45^{\circ}+A\right) \cos \left(45^{\circ}-B\right)+\cos \left(45^{\circ...
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Prove that
\[
\sin \left(45^{\circ}+A\right) \cos \left(45^{\circ}-B\right)+\cos \left(45^{\circ}+A\right) \sin \left(45^{\circ}-B\right)=\cos (A-B)
\]
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