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2.2 Trigonometric Substitution

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2. 2
TRIGONOMETRIC
SUBSTITUTION
ZTri-gonometricsubstitutiffk.ca
2.
)ok
Express
trig
2
×
in
terms of
function
#
{
=
cost
2nd
of 0
62+012
012=5-62
cÑ
d=F
C?
d.
a
=
Sino
%
-
_
Tano
a×ÉEi
①
②
③
?⃝
IFE ok
¥"
oi-j
Ecos
=
ÉÑ
at
sino
-
=
a
=
a
0
•
so
sin 0
¥+17300k
②
FE
¥É¥
+0¥
✗
=
cos
¥q=
=
sin 0
¥-0
=
a
cosec
0
Tano
=
FE
=
¥
=
+÷g
=
cot 0
c÷o=a
0
•
a
TEXTBOOK
to
ra ¥0
=
atac
③
Fti
F5
¥
×
=
tano
x=aT
Foi=asec
q=
¥
=
"
SO
Coto
¢2
=
TEXTBOOK
✗
a
=
cosec
a
cot 0
0
*
✗
=
☒
as in
€2
=
a
:
→
d✗
=
a
cos
0010
cost
.E #*c*o-*o- EifE.odoa1afcosec20dO- 1if-coTO)+c
↓
=
-
fi
cot 0
+ c
=
-
¥
+
-
=
-
+ a
c
16=42
E
•
=
du
=
→ Q
=
4
"
S
dx
=I*¥÷÷=Iu¥:°"=*
he
,
du
=
¥16
*
=
=
•Tan
=
0=4Tano
4sec -0 do
4sec 0
=
=£*¥:É¥ =¥I:¥ :*
cosec
tzln /
0 do
-
=
%/
1¢
In
+C
"
/ cosec O cotbltc
=
-
flu 125×2%67--4,1
,
+
C
EF¥¥¥≠
$
ok
✗ 2+8×+16
,
(
U
:=
✗
1- 4
yu¥,
¥9
u
>
=
=
=
=
=
die
→
3
=
@ at +
+
4T¥
→
du
sec
0
=
3
Sec
0
+
Tano
13 /
I
+
In
/ FÉ+Ñ+z* / ten
but F.
txt
41
-
bin 3
do
=
G-
/
ten
do
•
In
+
"
sec 20
↑¥;¥÷ -1sec
In /
9
ok
=
da
3 tan 0
1-25-16
=
+ Cn
hnla.lt C
=-
✗
dx
€+8TI :¥¥
=
a
Sec 0
=
¥0
+
C
=
¥
a
=
→
>
a
=
=
✗ 4-
Tan 0
sect do
a'
=
oiseio
¥-11010
tan
"
¥
+
C
+
c
-
f ¥+7.0k
=
¥ tan -1¥
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