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Contents
Addition Formulae (Cosine)
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Addition Formula (Cosine)
cos (A + B) = cos A cos B - sin A sin B
cos (A - B) = cos A cos B + sin A sin B
Proof
of the Addition Formula
The
formula can be proved geometrically. However, since we have proved the formula
for the sine function, we can make use of it to prove the cosine function.
cos
(A + B) = sin [90o - (A +
B)]
complementary
angles
= sin [(90o - A) -
B]
regrouping
of terms
= sin (90o - A) cos B - cos (90o - A) sin
B addition
formula for sine
= cos A cos B - sin A sin
B
complementary
angles
Replacing
B by (-B),
cos
(A - B) = cos A cos (-B) - sin A sin (-B)
= cos A cos B + sin A sin
B
negative
angles
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