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EE=
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9CqL)
A
cb)fca.i oJ'®8 eq`~a) c5a® fc*'3 ag6eGd 83a@6G
pct9 = jfx,4+ a`x3+bz2_2iz-4
ci2i-n , pciL> g ®3@ae6ap ®@ pcn=o©
PCD = I+a+b-2-4`=O ©cl+b = 5. -> a
cqLt2) , pc*> g Leso@aecsal 8]@ pG2)=o©
16 -8CL + 4G +4~ 4 '= a
8a-4b =16
2a-b = 4 -©
a+©
cfl)
3a-9=3©
b= 5-3
b=2©i- I___-
zA
Pcqc) = c2L4 + 3CL3 + 2%2 ~2~ -4
= C*-I) C*+`» CA*'+BZ+C) ®
i850CE#eo 6zi5€®
q7 =A©%7 38-=:+a--6Csg'' i= 2 ©
•®. pci)= cz-nc*+2)c*2+2%+2?©
C8)
\
Cg)
al)
Clo)
CC) Jz2+bar+ C=O
o< + p --b ©O`p-a ©
3£ er> i ©eeym ®8j2s>6he!cs
CrL~ct3.CEL-i.=O©
zQ_ 2 co{3+ F) tl[otp)3=o ©
X2 -EL CBbc _b3) + C3+~_a
a,3+ i o( 3 p3+ ,
P3p3
©o{3+p3 = cot+p)3 -3o<PCo<+f)
= C-b)3 -gc C~b)
--b3+3bc®
c3+I
cr3F3+l = ±a(3 of3
g = C{fi) ©62}B3©rfeas ®3@ae6caed, @3L
fa = (c3+, )J
[Cg)I a _ ( CL¥ ) ( 3 bc -b3) + C3 = o
|C3+I)2 _ Cc3+I).C 3bc_b3) g + C39£= 0
9->*c3*2 ._ cc3+I)c3bc-b3jtr +CC3+I)2=o ©
HE=EE
//
E
z4
Cb) cr = 2 CO-Sfn®)
= 2 C I -Coser) ©
T= k # ©2 S,n a ©2 C , -Cos 0) ©
± a-in c>/2 cos®/2
2 Srn 2 er/2 ©cot er/i
-_ _ --
CW, a 2g
dz2
g= 2Cl-Coser)
± = 2 Srn8r ©do,
ct,,, (±)®=E = eat(g,8-g©
(#)D=z = -a Cosec4(a)a.
-i x. IG
ddz ( Cot 9/2 )
£ ( cot 9,2 ) . d= ©_ cosec-_e/;2 x i x
©_-_ - cosec:2e/2
2
4 xr 2 Sm3 9/2-+ cosec4B/2 ®
EE-
2cl-case)©
®
CC) tzi2+g2~ 4z+69+7=O.
2z + 29. dL±± _ 4 + 6c a+± = adzdl
Z + Cg +3) -dLj± = 4dtz.
I + Cg+3) C12LLg1
dtL2i #* 1 #ey ) - a ®
cg +3' 4± +(#11+ , -o ©d.z2
++-..-
zA
\
•Z<1 I < 9C < 4 .Z>4
i "c tr) aeeae C-) C-) C+)
f es8 ga2De f cs8 g®2o@ •F e@ g®sD@
GS ©§ 6§.
A{r) = 27rr2_ .r2 + 27Trh
= (27T-I)r2+ 27Trx a?
ITr2
C27T-I) rsL + 54__
r
(27T-I)*Qr i 54__.I
r2
ITrs2h = 27
h = 2-+-__.
7rr2
± o <j (27T.-i) 2r -jL± =or2
r3 = 21I-I-( 2 7T i I I)
r=33 ( 2 n ,- i )
o<r<- r> =k,- 97,-I
±<o dLi >oc],.gr -dr
®©r=3
27T-I
§0 -- A 9®@ ©8. ©
Cos a -Cos 2c> = en 9CL-
2 a-in a= *eio = -_ 2 eta 3= c:== 3=&2`©` + -
Sin 9]3ro ( 5In a/2 - COS 3®/jL)
S,`n3G>=o 6coB Sine/r2~ Cose®/L=o ©2
Srn 3e = em a__
EI
± = n7T+C-I)r}.a26r = 1nfi
33 n€Z®
Cos 3LLa = 3m ®/2EE
Cos 30c2
3eL=__EEI
I cos (¥-=)
2mIT±(= -±) ; in€2P.
©+/ gel _ 2rn7T + ZL -±=-2220 = 2m7T +J|,2
®= mIT +¥ 3 rnez.I--i
-/ gel __--J2
a
2m 7T ~ .7T + ±E-222rn7T -"I_2-- za_-------_
" tan-I('±)-tan-I(±) = tan-`(i)-tan-`(i)
tan-` (± ) = Ol
tanoL = -`Z_1
+an-i(±,|=p +an-'(i)„ ton-`(i)=8
®®83 a <c* , p , or , a < 7T/1 era .
tanp= i'jzr + I
©mangr= i lfln£=|53
o`-p= a--a
Tan (o<_P) = Tc]n
Tan o< -Tan F
I t Tan o{ Tan P
I_ _ __ .
ctL_i) Ctz+I)
I+1xLCtr-l') (3Ct')
cJ-„ ©Tan I - Tan J't + Ta ri J Tan J`.
i - '/3St 3w5 X, I/i
4=_--'8
%2 = 9 ©fz=3 ( 2<ZZ4)i_ © -©edap
Cb) fcqn = 3 Csrnq -Co3Ji)4+ 6Csrnc[+Cosi`)2
fca = 3[(Srnq_cog±)2]2+ 6 CSFntt +co§Tz)2
= 3 [ Sin2z + Cosfz -23fr)ticosi ] 2 + 6 [Sm3ir+cos2*- .. J` -L©
= 3 I I -Srn s2rz ]2 + 6 [ I + Srn 2t] ©
= 3 [ I -2 Sin 2* + Sin2 2rz -] .+ 6 + 6 Sin '2*
3 + 3 Sin' 2z + G
9+3 ' - CO 3 4Tt2
-g+=(,-cOs4*)
-L|-±CoS4*022
©®6 A= 2, g 8=-iE±
©2©
©+2S{nttcos
rIil1((
g c tz`) = 2 5 - 2 f c1)
= 25 -2 (i _ = Cos 4Z)
9cz)= 4+3CoS4* g e88®@ae a©ee
9 99© e2EDs a@a ©1 eni®c5a ©
- ,- -- - - - - -- _- - - _ - _- ---
`ir__ ___,,+ , #alcoGe&a© z9(tz)=I
t--.+.-...-,-,-- I-------i-@--.>=
-tr/2 -3trfe -nz+ -7rvsfcil)=12gcaL)=25-2C12) a tr ;e nz4 3 Th;¢j TT;2=,¥|563esesape§ag©40
gc*,-I ®
®®. fct['>= `2 a62D6zi3cs® [-
c5eaal 5®rfe. ©
I
i
STr, i -COS (¥) = -2Srn i STn i2
I.AS -SrnA _Cos (B±C)2
= Sin (¥_ (BL=)) _ Cos C=) ®
Cos ( ¥C ) _ cos C BL=C ) J ©
= 2 Srn(±) Srn (-±) ©
• -2S,.n Ji s- i ®22
<__-__---'------_
binAgo c a
CL"en®s±=&G¥al=ea¥6gaa=&as&asen©esch-b
At) = b Sin A
ArD= a Sin a
•.. bsmA =asmB
©
AD = a Srn 8
AO= b`
ArD = bx.I
AD = b*SmA CA =9o.)
•., b Si'n A = a Sin 8
®
AD= b Sin C7f .-A)
AD = b3rr}A.
•.-.'b Srn A = a Sfn a
®6©©@®© b 3rnA = c3fn a ®© i59®cOCS @e 8>ten
STr} A Sin a------ = _ - =ab
SfnCI_,
C
4
Ca+b) tan (¥) = CCL-b) tan (A+B )
CL+b = tan (¥8)__a-b tan (¥)
L`H. 3 a+bE-a-b
k 3rn A + k3inB
ksmA -k3inB
- 2 Srn (AL¥)
a®©
©cos (¥8, ©
2 Cos (¥8 ) Srn (=
= tan(¥)®#©)©
Ccl+b) „n (PL=B) = CcL-b) +an (¥8 )A®ai',5-o ::
ir ++ +
