Page 63 - Math Grade 12 (Advance)

PROEUS DARA
= (cosx- sinx)sin2x- 2(sinx+ cosx)(cos2x)
2
(sin2x)
2 2
( cosx sinx)(2 sinxcosx)- 2( sinx + cosx)( cos x- sin x)
= ~------~~------~~--------~--------~
2
sin 2x
1 2
= - - -(cosx sinx)[2sinxcosx-2(sinx+ cosx) ]
2
sin 2x
= -;-(sinx-- cosx)(2 + sin2x)
sin 2x
tn sinx-cosx = sinx-sin(~ x) = 2cos~sin(x-~) = J2sin(x-~)

i:ltH!:H y' = +J2sin(x- ~)(2sin2x) L?itl X E R ' -1::; sin2x::; 1 ,
u
sm 2x
2
tUi ru sin 2x > 0 '1
~mag y' 'tllanHJJl~u sin(x-~) '1

sin(x-~) = o ~~stl x-~ = krt, kE z

3rt
rt
trn "" X=- -rt = --
""' (-rt, rt) , m k = -I ,
4 4
"" rt
m k=O, x=
4
t rn < -rt, rt) fil?it'Utl sin2x 'fa y

3rt
-rt<X<--
4 '

3rt rt rt 3rt
-- <x<-- -rt<x-- <-- sin(x- ~) < 0
4 2 ' 4 4 '
3rt
rt
rt
""
trn (-~, 0) ' -~ <x< 0 -- <x-- <-- sin(x-~)<o
2 4 4 4 '
.., 0 rt
trn (o, ~) , sin(x- ~) = 0 mmg X=-
4
rt
O<x< -~ <x- ~ <0 , sin(x-~)<o
4 ' 4 4
rt rt rt rt sin(x-~)>o
-<x<- , O<x--<-
4 2 4 4
trn (~, rt) ' rt rt 3rt sin( x -- ~) > 0
""
-<x--<-
4
4
4

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