1. $8sinx=\frac{\sqrt{3}}{cosx}+\frac{1}{sinx}$
2. $2cos^{3}x+cos2x+sinx=0$
3. $tanx-3cotx=4(sinx+cosx)-2$
4. $sin^{3}x+cos^{3}x=sinx-cosx$
5. $cos^{2}x-4sin^{2}-3cosxsin^{2}x+sinx=0$
Bài 1
ĐK:   sinxcosx # 0 <=> sin2x #0
8sinx = √3/cosx + 1/sinx
<=> 8sinx = (√3sinx + cosx)/(sinx*cosx)
< => 8sin² x * cosx = √3sinx + cosx
< => 4sin² x * cosx = (√3/2)sinx + (1/2)cosx
< => 4sin² x * cosx = (√3/2)sinx + (1/2)cosx
< => 2sinx * sin2x = cos(x - π/3)
< => cosx - cos3x = cos(x - π/3)
< => cosx - cos(x - π/3) = cos3x
< => 2sin(π/6) * sin(x - π/6) = cos3x
< => sin(x - π/6) = cos3x = sin(π/2 - 3x)
Giải tiếp nha em
Chúc em học tốt!!!!!!!!!
Bài 2: 2cos3x+cos2x+sinx=02cos3x+cos2x+sinx=0pt:
<=> 2cos^3x+cos^2x-sin^2x+sinx = 0
< => cos^2x(2cosx + 1) + sinx(1 - sinx) = 0
< => (1 - sin^2x)(2cosx + 1)+ sinx(1 - sinx) = 0
< => (1 - sinx)(1 + sinx)(2cosx + 1) + sinx(1-sin...
< => (1-sinx)[(1+sinx)(2cosx+1) + sinx] = 0 
<=> 1 - sinx = 0 (1) hay (1 + sinx)(2cosx + 1) + sinx = 0 (2)
(1)1 - sinx = 0 <=> sinx = 0<=>x = kpi
(2) (1+sinx)(2cosx+1)+sinx=0<=>2cosx+1+2sinx...
< =>2 (sinx + cosx) + (sinx+cosx)^2 = 0
< => (sinx + cosx)(2 + sinx + cosx) = 0
< => sinx + cosx = 0 hay 2 + sinx + cosx = 0
Giải tiếp nha em.
Chúc em học tốt!!!!!
Bài 4
$sin^3x+cos^3x = sinx - cosx$
$< => (sin^3x-sinx)+(cos^3x+cosx) = 0$ 
$< => sinx(sin^2x-1)+cosx(cos^2x+1) = 0$ 
$< => -cos^2xsinx+cosx(cos^2x+1) = 0$
$< => cosx(-cosx.sinx+cos^2x+1) = 0$ 
$< => cos = 0$ hoặc ($-cosx.sinx+cos^2x+1) = 0$
Em giải tiếp nhak!
Chúc em học tốt!!!!!!

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