Identities Sheet

Fundamental Derivaties
TriaIdentifies
Double As a
of Inverse Trig functions
- -




tan-si * [Sint 7 Fu u


cos(26) = cost -
sin6 *(csu) :22.
- I
1- x
2 tanf
cot == En tan (28) Franco
=
* [tan"u] it =
I




[esn] :
r

since
u2 -1

sin cos
S
I
ese = see -


,




2


Sin'Escos 8 = / tan() =
M
·
1 - cos' 8
#Eric
Frig Functions
-
Sin 8 =
.
(25] x


sinto- Hes
-


e
coso = 1 - Since 2
Sinhx = -


2
es(20)
+




i
coso-
2 2
(20)
tan 8 s 1 = See 8 tano-I-cos
& (20) - cos


tanto-sees-I
see'D-tano = I
Integration
Frigonometric Table

Ssinxdx = - cesX + c



cott) =
cs28
ScosXdx = sinx o


cot20 = eso-I Stanx dx In/seex) = b Trig Identities
Hyperic
(scO-coto =
/ Sseaxtanx seex = + ↳ sinh(-x) = -
sinh x


Scsexcotx dx = -
cex + >
-


cosh)-x) =
cosh x




!
sin(-0) -Sind dx
see'x tanx coshix-sintix /
=
>
c
-
= + =




cs)-0) -esO =
usex dx = cotX +c >
-


sinh(x +y) Sinhxcoshyo coshxsinhy =




! lu/cx-cotxloc
tan(- f) tanf dx cosh(X x)
esex
>
coshxceshy sinkxsinhy
-
= = -
=
+ a



cot) 8) = -
co to see dx In/seax tanx/oa
x =
o
>
-

Sinh2x = 2 sinhxcoshx
cos)- 8) : cost Scotxdx lu/sin x loc = >
-

cosh2x = cash2X o Sinhix
see( 8) - = Seco >
-

coshix =
&(1 cosh2x) +


use
Try functions - >
sinhix = (1 cosh2x) +


( 1]
&




Sum : Difference
-
Formulas sin(sinix) = x +
1
,


( 1)
-




cos(X +
B) =
costcosB-sin Sin cos(cos"x) = X -
1
, Calculus
of HyperteTrigeunctions
cos (X-B) :
costcosBe sind sink tan(tanix) =
x [-x x] , [sinhu) coshu * =
I




Sin (B) =
Sinsing -
s Xest sin"(sinx) = X [E ,& * [coshu] = Sinhu d -


X


sin(X-B) =
SindsinB a cosX cost cos" (losx) = X [0 i] , [tanhu] =
sechtn .
tan" (tanx) = X
( -




[eschu] = - eschu ethu . 7




tan
tan(x-B) eas es(csix) * [sech u] sechutanhu .
-




= X =

tanxtau
-
=




[cothu) eschin E
-




see(sex) = X = -
·




tanx-tan




,
tan(X-B) =
ct(ct"x) x
coshu du sinhu
T
tano
=

& tanB
=
+


csi'(cxx) = x
sinhu du = coshu + a


see"(secx) = x sech'u du = tanhu x


cot (c+ x) = X
eschu cothu ·
du = -eschus a



sechn tanhu . du = -Sechu oc


eschiu du =
-cothu -c