Question

Derive the property

cos(AB)=cosAcosB+sinAsinB\cos (A-B)=\cos A \cos B+\sin A \sin B

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Solution

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Let dd be the diffrence between the points M(cosA,sinA)M(\cos{A},\sin{A}) and N(cosB,sinB)N(\cos{B}, \sin{B}). Angles AA and BB are in the standard position in coordinate system and points MM and NN are intersection points between the unit circle and the angles AA and BB, respectively.

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