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The compound angle formulas expand a sum or difference into products of single-angle values: sin(A ± B) = sin A cos B ± cos A sin B and cos(A ± B) = cos A cos B ∓ sin A sin B. Note the sign flip in the cosine version.
Sine
sin(A ± B) = sin A cos B ± cos A sin B
Cosine
cos(A ± B) = cos A cos B ∓ sin A sin B
sin 75° ≈ 0.9659258 and cos 15° ≈ 0.9659258 — the same value, as sin 75° = cos 15°.
It follows from the rotation matrix product; geometrically, adding angles reduces the cosine while it increases the sine near zero.