Point P is at an angle \alpha from the positive x-axis with coordinates \left(\cos \alpha ,\sin \alpha \right) and point Q is at an angle of \beta from the positive x-axis with coordinates \left(\cos \beta ,\sin \beta \right). Let’s consider two points on the unit circle. \cos \left(\alpha -\beta \right)=\cos \alpha \cos \beta +\sin \alpha \sin \beta įirst, we will prove the difference formula for cosines. \cos \left(\alpha +\beta \right)=\cos \alpha \cos \beta -\sin \alpha \sin \beta We will begin with the sum and difference formulas for cosine, so that we can find the cosine of a given angle if we can break it up into the sum or difference of two of the special angles.
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