Page 96 - Math Grade 11 (Basic)

PROEUS DARA

2.1 itJUSYBU
u n • 1

n. &1=12~ a=~ dStu ~ tthl15 a nh:iti'i:3S sin(a+~) tl=ltnS
u 1.1 "' u "
1
sin2a = sin( a+ a) = sinacosa + cosasina = 2sinacosa '1
~msg \ sin2a = 2sinacosa j (7)

2. ttltl=ldStu ~ tthru a t9inh:iti'i:3S cos(a+~) tl=ltnS:
1.1 "' u "
1
2 2
cos2a = cos( a+ a) = cosacosa sinasina = cos a- sin a '1

2 2 2
cos2a =cos a-(1 cos a)= 2cos a '1

(8)

1'!1. ttltl=ldStu ~ tthl15 a t9inhams tan(a+~) tl=lt[lS
1.1 "' u "
1
tan a+ tana 2tana
tan2a = tan( a+ a) = = '1
2
tanatana tan a
l::ltHS8 tan2a = 2tana (9)
2
u l-tan a
"" .., 4 "" :It
~n sin2a ' cos2a sh tan2a m cosa = - 5 sh 2 <a< :It '1

:It
tthru <a<n =
2
4) 2
. 2
2 .
<.J<-:>roo
. Hl)( 3 <t
stn a = - - - = - , w u • ~ o sm a = smacosa = 2 3 ( 4) = - 24
x
x -
. 5 5 u 5 5 25
2 4 2 7 sina 3
cos2a = 2cos a- 1 = 2 x (- ) = - ~ tti'Q18 tana = -- = -- ~
5 25 cosa 4
iJ§~ tan2a = 2 tana = 24 '1 tl=lffimn tan2a = sin2a = 24 '1
u 1- tm/a 7 cos2a 7

"'
!J Enuu nn 2 l=ltlil81 sin3a sh cos3a '1

sin3a = sin(2a +a) = sin2acosa + sinacos2a
2
2
3
2 .
2 ·
(I 2 .
.
.
)
.
= 2 smacosacosa + sma - sm a = smacos a+ sma- sm a
01