G eometry (see Appendix A, page 1015)

Fundamental Identities
I
CSC B^
2- sec 0
cot B
3
tan 0
4
5 cot 0
1
sin 0
• 1
9
sini-B) = -sin 0
19
sin(a + ^) = sin a cos /3 + sin (3 cos a
10
cos(-0)==cos0
20
cos(a + (S) = cos o; cos jS ~ sin a sin jS
11 tan(-0) = "tan 0
cos 0
21 tan(a + /3)
12 cot(~0) === -cot 0
1
tan 6
13 sec(-^) = sec B
sin 0
cos 0 •
22
sin 0
COS'^ f ? +
sin^ 0 = 1
7
1 + tan^ 0 = sec^ B
1 + cot^ 0 == csc^ 0
15 sin 20 ==
16 cos 20 =
=
=
2 sin B cos B
2 cos^ 0 - 1
1 - 2 sin^ 0
cos^ 9 - sin^
24
sin(a - ^3) = sin a cos ^ - sin /3 cos a
tan(a ~ (3)
tan a - tan (3
1 + tan a tan (i
Product Formulas
17 cos^ 0 - 1(1 + cos 20)
18 sin^ a = k l " cos 20)
Geometry
1 ~ tan a tan /3
23 cos(a - /3) = cos a cos /3 + sin a sin ^
Double-Angle Formulas
COS 0
tan a + tan IB
Subtraction Formulas
14 csc(-^) = -CSC 9
6
8
Addition Formulas
Even-Odd Identities
25
sin a cos jS =^ |[sin (a + /3) + sin (a - (3)]
26
cos a cos /3 = |[cos (a + /3) + cos (a - ^3)]
27
sin a sin /3 = |[cos (a - /3) - cos (a + (B)]
(see Appendix A, page 1015)
DM
1
D^u" = nu" ^ D^u
11
Z)^ sinh u = cosh « D^u
2
D:,{u + v) = DxU + D^v
12
Z?:^ cosh M ~ sinh M Z^^^M
3
/>:((HV) = uDxV 4- vD;,M
13
Dx tanh M = sech^ u D^u
14
Dx coth u = - c s c h ^ u D^u
4
D,
15
Dx sech M ™ - s e c h u tanh M £>J,M
H N __ vD^u - uDxV
7/
^
i^
5
D;c sin H = cos u D^u
16
Dx csch M = " c s c h u coth M Z);t«
6
I>:c cos u = —sin M DJ;H
17
D;,e" = e" £>;,M
7
Z)j: tan M = sec^ M Z>;CM
18
D;,a" = a" In a D^u
8
Dx cot M = ~ c s c ^ u DxU
19
Z);, lOga M
9
D;r sec u ~ sec H tan u DxU
20
Z>. In M ==
10
D^ CSC u = —CSC M cot u D^u
uln a
DxU
u
27 Dx
f(t)dt^f{u)DxU