Angle addition identities
The trigonometric angle addition identities state the following identities:
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Contents
[hide]Proofs
Proof 1
Proof 2
Let point and point
be two points on the unit circle such that
.
By the law of cosine, we know that:
Apply the distance formula to obtain the length of :
Substituting and rearranging to get:
See that the identity holds true (and makes sense geometrically) when due to the fact that
.
Then, let and substitute it into the identity and the angle addition identity for cosine follows.