This document contains mathematical equations and expressions involving trigonometric functions such as sine, cosine, and tangent. Variables such as q, b, C, and r are used in equations representing relationships between various trigonometric ratios and algebraic expressions. The document also includes equations that are summed, factored, and simplified using trigonometric identities and algebraic manipulation.

1. A. -U1ttf -- _
' loo,Qt,0z---
C-7,7t5,8-"'
* ) cttJab r
6 -Llrltf
q: -U, h: q
L,{u
= Gl tn,-r)h
= -Ll + { H-r) lr
= t-lt*f;;gG
C" 7, 7r !'r e
Cl:7,b: t)tb
Ll ril = Ct r Cfl ,-r ):b
1 '=',', 'o 'ru,l't
' iz
4='l0u r b;-e q= qg b r-tg
QtzA+tn-r)! ()rt= a+Cn_r)}
=l0atctt-t-q =qga(1-r)-rd
t
z t)a *90: {O. : grS r L-i?o) _- -B?
?" 9Ualu batrran qttt(natr Mo?Qhur subo ve 7 = G a a n )tr?u be 7z =
g& Lon+uzantlh Stteuawat n boc,lanv4
Utr=O :) ct,,+&b:S &"t& b: tr
U?r,€U :) o{ztb=q0 {-LV6 g:8
:irbr-eA 'A+56=8
b: 6 a: -20
q.e 113ltd-f ..
b. I oat tcJo tt00{ --
c'-rtzt 4J-'
-7tr +to tl6'5 J' .'

2. 5o:
:
C
t4 TonpuVsnteh
7ao
q=io3
Un= tqC)
37 =
q"6+15+t0
5n?'hn(?a{(.n-r)
e:8
b:5
,fzg(7.9+(d-r)5
("{
L l6 + {t ) 5
? q t t b + I y )
ftn ? (/z n ( A { Ct-rp )
: tl 5l '- Lcul
rBCa
6,)-
=,ZtO
3
*i ) tc
' o l- 19 a4 t$b ..i
q
' Too
b*- ro
Sg: tlt0tZ^aoa ") (g
] Lt ( 4oo + Lz ) rC) )
: E( uou +2t>) =
-71'r
2
5 t 8('l'*Yt-(E i)T
= -iu t' (-l )l
= (*tt)+uct ) = l5L
3 L (fr>
{. 6tf
6 ,5 )
0 (L
{1r
{_1 I
+ lb,
et)
)u mrch {)k ofr
0 = t7y
b---3
(,rn ? Lg Cl
qM'i tffi (#r b&t Vo tt ?ci+ a n T
rclcl = tDS.t ( n-r ) 5
q n to rfi {ua $r-{
lQet =iul+ ln 3
nz q::
?J
3T
tqq )

3. -q
"ltu
gooff)0*ri €rtvut
q: ltt'!rl6 - '-
0": [ , Y": l-l
Utb: cl"P[n*i)
: I'q(1t3*t)
:l qq :l&ztutl
(7 '
I V 7 '-'J-
() f c n - L)
1 L-z)
q
€ 153 b
. [UC:r? U/14
q ? tuo , V: !
5
( tp -l)
, QA,'Lt 0 r Lq
a=qd
lr= l,7
(/ Lo: luU.
r o z c) 6[*+ )q
tU ; E
tJ -r 517
OrlDTS-
" scr c{-lu botljCI n
kcrnluvan{dh
tc rt ,uuo
c,l r Unye
ku L:7zQ .-i an |vt tu to
t"{ ?,= 1zg
1'- 3
?) av =
179
3
LLl
(
I
y{
VT
V=
f : -.,lS
a h = 1zc)
7): T zcl
lA"= 7

4. Qt,tYtt ( :
d"${t(}rJ?r
" 'tue rsou + Uro t
C- -f + tU -Lu +'.
' u + t y t 5 t
)a u/a
q- S +(6{ jTL L
Az I n:tp
!-: L
Stb: q P0-t)
t'-l
SLo: I ( )
z*l
: B ( t) '- dtgq
I
" TUotJtlci+ ttSO
q>zoo n?tc
"bzIrx-
StD: ZaD )
irt t
: 2as ( )
e t y
= ZSu6€
toJuVu ?e,Yto q
( c*S+[u*Zu +tP
q
=
* f
Y = *7
5 rb ?
[ - c-z)
z - f ( tu?>* )
3
: el 0s,33
LIS + Lr + t + * ; . i^
q=u5 p? to
Y=J
3
S io = qf C
L- I
Sto = ,l ,ob x

5. );ci { t f,_
d: 'Lll
t-/q
s: ot / t i-L-)
:) I +Urun
il": 5U (W,1
V: 7['s
5t : d / th-r)
-_ r5D l( [_7lS
z trc {f ,/s)
Vt'tethrn€fci c4 kovtVLA{ t{7j
i l/ +
lqI{
rllTlq: tbis
9 fiaiv
; l OrO C
Y -- 7-I )
5 z .A I ("t-v )
= tuo t ( t - z{z)
: uu i t'l ) :
v)
(4 I L I < t/q ) :
b 5-tt +qr I
va L c1 Q lt
Vo tcrrl+qt " )tVa botA ryomantut Ve mbatt al| Qr. botrnqqta0
gObotufnOVa" TAntubatoh pct0)crtgtqh PAntgt0A l1vt1s1 tott yq
)
= Vf r: C
5 : ) 1 | r'?
^3 t-[ f b + rrS)C
z 7fo cffi : 7rf

6. Li(3i-t{)
( Iz tts I )
7
: qqT u
Q 6 A
& t?qo)
')
tltl1"r r)
)=atlT{-i
)f jui-
t i'-
Z
i2
"[2
I y ( [r + t
:( )
I
r S(
7-l St -Lt :
:
:L
--b ( 4,
t:l
tc v lc 'P lL',T Y
q't
('
3
:&
iU. [-t Itu vl c]wh
q7
i--l
)a w0b
A: 5= 7*.5 ) =
sat
l2
[:!
L
z

7. IO hunaVdn tQorCIft1o
cr ()srn tr)3
U, (_)si.11 g)i.o
(.[ )sin t])c
& { ) r nn f} 3/
rk )AWab
7
( ) e rrr 0 )
3
:
Derny w Y8 Lr n tuv ryl€ nv &taay n nq s f
SuVD Vostn us darrr Vcr'tPato.tr1- P
)5rr1 g@- 3(o50 )
t-r7k1 + J
z 3 1t-t
t
E
I
K
rz l)7
-L z3 !€ 97-z* I r
€ Z"
J f 7i zZ r 3 ,-
81
] (z:l )- i(7
8 vs
I { )?sln 3 CI E 3
E
( zc$i g )
(z- )
'?.
z tt z 7t
f t zL 7w '! i-1r
: (?-14+l r t4t?1- r_l ) +t )
tt?Ll 7
- t 6 zcugLtU ^Llt)?- trn ?.9 +(
'^ r-
lb
,-n t (cosqA* {"ufufutr'{fl0 +L )
E
;_l (
Y
) jin 0; IL
I
b
,L

8. (. ()l,p X; =
)srn 0 : J- ( z--L
t)x,
t) )nn )s)(f {L!))5
7 7L Zs Zq
J
7s
:(
it
5 (u-9 30 + ) ic 5; n {)
T7
? t/.t ( ) srn b u -
(llin 0)G 7
( ) tr n u )
&
- (I iz-r ))L
^L -L
.l
6Lt
:l
u
:t ?t z3 7Y
Lz- *,1 )
ar ,e
7tZ
71 z't
[q ( Zctss fr O- ( qdin qO) I t] [ 2 cog z0 -zo)