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cos( A
±
B )=cos( A )cos( B )
sin( A ) sin( B )
tan( A )
±
tan( B )
tan( A
±
B )=
1
tan( A )tan( B )
sin(2 β )=2sin( β )cos( β )
cos(2 β )=cos 2 ( β )
sin 2 ( β )
cos(2 β )=2cos 2 ( β )
1
2sin 2 ( β )
cos(2 β )=1
4sin 3 ( β )
sin(3 β )=3sin( β )
cos(3 β )=4cos 3 ( β )
3cos( β )
cos 2 ( β )= 1
2 (1 + cos(2 β ))
sin 2 ( β )= 1
2 (1
cos(2 β ))
4.8 Perimeter Relationships
Finally, referring back to Figure 4.3, we come to the relationships that inte-
grate angles with the perimeter of a triangle:
S = 1
2 ( a + b + c )
= ( s
sin A
2
b )( s
c )
bc
= ( s
sin B
2
c )( s
a )
ca
= ( s
sin C
2
a )( s
b )
ab
= s ( s
cos A
2
a )
bc
= s ( s
cos B
2
b )
ca
= s ( s
cos C
2
c )
ab
 
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