Question

Tolong bantu kerjain no 9-11 yaa

Answer 1

Verified answer

No.9
3 tan⁴x - 4 tan²x + 1 = 0
misal y = tanx
maka
3y⁴ - 4y + 1 = 0
(y - 1) (y + 1) (3y² - 1) = 0
y = 1
tanx = 1
x = 45
, 
y = -1
tanx = -1
x = 135

3y² - 1 = 0
y = -1/√3
tanx = -1/√3
x = 150°

y = 1/√3
tanx = 1/√3
x = 30°

jawab : C atau E

No/ 10
2 cosx = 3 tanx
2 cosx = 3 sinx/cosx
2 cos²x = 3 sinx
2(1 - sin²x) = 3 sinx
2 - 2 sin²x = 3 sinx
2 sin²x + 3 sinx - 2 = 0
(2sinx - 1) (sinx + 2) = 0
sinx = 1/2
x = 30° ; 150°

No. 11
tanx = 2 sinx
sinx/cosx = 2 sinx
sinx/cosx - 2sinx.cosx/cosx = 0
sinx - 2sinx.cosx = 0
sinx(1 - 2cosx) = 0
cosx = 1/2

sinx = 0
x = 0, 180, 360
cosx = 1 atau -1
jadi
cosx = -1 , 1/2 atau 1

Answer 2

Jawabannya:
9. 3tan⁴x-4tan²x+1=0
mis y=tanx
* 3y⁴-4y+1=0
(y-1)(y+1)(3y²-1)=0
y= 1
tanx= 1
x= 45°
* y= -1
tanx= -1
x= 135
* 3y²-1=0
y= -1/√3
tan x= -1/√3
x= 150°
* y=1/√3
tanx= 1/√3
x= 30°
Jawab : C

10. 2cosx=3tanx
2cosx=3sinx/cosx
2cos²x=3sinx
2(1-sin²x)=3sinx
2-2sin²x= 3sinx
2sin²x+3sinx-2=0
( 2sinx-1 )(sinx+2)=0
sinx= 1/2
x= 30°, 150°

11. tanx=2sinx
sinx/cosx=2sinx
sinx/cosx-2sinx.cosx/cosx=0
sinx-2sinx.cosx=0
sinx(1-2cosx)=0
cosx=1/2

sinx=0
x= 0°,180°,360°
cosx= 1 atau -1
maka cosx= -1, 1/2 atau 1

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