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Contents
Addition Formulae (Sine)
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Addition Formula (Sine)
The addition formula for the sine function is the basis of all the formulas in this section. It can also be used to prove the supplementary and complementary angles identities. We will provide a geometric proof of the formula. 
sin (A + B) = sin A cos B + cos A sin B
sin (A - B) = sin A cos B - cos A sin B
Proof
of the Addition Formula
 c
= a cos B + b cos A
apply
trigonometric ratios to the two right angled triangles that c borders.
r
= 1/2 take
the diameter as 1. r is the radius.
sin
E = (c/2)/(1/2) = c
sin
A = a, sin B = b sine
rule; since sin E = c, c/sin E = 1
Hence,
c = sin A cos B + cos A sin B
sin
(A + B) = sin [p
- (A +B)] supplementary
angles
= sin E
= c
= sin A cos B + cos A sin B
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