Difference of Two Angles Identities
This figure illustrates the “proof without words” of the difference of two angles identities. To construct this figure: see this example.
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The difference of two angles identities express the cosine and sine of the difference of the two angles in terms of their individual components.
To derive the difference of two angles identities, two right triangles are placed next to eachother so their angles sum together to be one angle and one triangle's angle is the difference of the sum and the other.