Bạn đang xem: Pt lượng giác
(sin^23x-cos^24x=sin^25x-cos^26x)
(Leftrightarrow2sin^23x-2cos^24x=2sin^25x-2cos^26x)
(Leftrightarrow2sin^23x-1+1-2cos^24x=2sin^25x-1+1-2cos^26x)
(Leftrightarrow-cos6x-cos8x=-cos10x-cos12x)
(Leftrightarrow cos6x-cos12x+cos8x-cos10x=0)
(Leftrightarrow sin9x.sin6x+sin9x.sin4x=0)
(Leftrightarrow sin9x.left(sin6x+sin4x ight)=0)
(Leftrightarrow2sin9x.sin5x.cosx=0)
(Leftrightarrowleft<eginmatrixsin9x=0\sin5x=0\cosx=0endmatrix ight.)
(Leftrightarrowleft<eginmatrixx=dfrackpi9\x=dfrackpi5\x=dfracpi2+kpiendmatrix ight.)
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cần sử dụng phương pháp hạ bậc nhằm giải các pmùi hương trình sau :
a)(sin^24x+sin^23x=sin^22x+sin^2x)
b)(cos^2x+cos^22x+cos^23x+cos^24x=2)
Lớp 11 Toán Bài 2: Phương thơm trình lượng giác cơ bản
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a)(ptLeftrightarrowfrac1-cos8x2+frac1-cos6x2=frac1-cos4x2+frac1-cos2x2)
(Leftrightarrow cos2x+cos4x=cos6x+cos8x)
(Leftrightarrow2cos3xcdot cosx=2cos7xcdot cosx)
(Leftrightarrow2cosleft(cos3x-cos7x ight)=0)
(Leftrightarrow2cosxcdotleft(-2 ight)cdot sin5xcdot sinleft(-2x ight)=0)
(Leftrightarrow cosxcdot sin2xcdot sin5x=0)
(Leftrightarrow sin2xcdot sin5x=0)(bởi vì sin2x=0 2sinx*cosx=0 tất cả th cosx=0 r`)
(Leftrightarrowleft<eginarraynghiemptsin2x=0\sin5x=0endarray ight.)(Rightarrowleft<eginarraynghiemptx=frackpi2\x=frackpi5endarray ight.)(left(kin Z ight))
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b)(ptLeftrightarrow1-cos2x+1-cos4x=1+cos6x+1+cos8x)
(Leftrightarrow cos2x+cos8x+cos4x+cos6x=0)
(Leftrightarrow cos10xcdot cos6x+cos10xcdot cos2x=0)
(Leftrightarrow cos10xleft(cos6x+cos2x ight)=0)
(Leftrightarrow cos10xcdot cos8xcdot cos4x=0)
(Leftrightarrowleft<eginarraynghiemptcos10x=0\cos8x=0\cos4x=0endarray ight.)
(Leftrightarrowleft<eginarraynghiemptx=fracpi20+frackpi10\x=fracpi16+frackpi8\x=fracpi8+frackpi4endarray ight.)
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(sin^2x+sin^23x=cos^22x+cos^24x)
Lớp 11 Tân oán Cmùi hương 1: HÀM SỐ LƯỢNG GIÁC. PHƯƠNG TRÌNH LƯỢNG GI...
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(Leftrightarrowfrac12-frac12cos2x+frac12-frac12cos6x=frac12+frac12cos4x+frac12+frac12cos8x)
(Leftrightarrow cos8x+cos2x+cos6x+cos4x=0)
(Leftrightarrow2cos5x.cos3x+2cos5x.cosx=0)
(Leftrightarrow cos5xleft(cos3x+cosx ight)=0)
(Leftrightarrow2cos5x.cos2x.cosx=0)
(Leftrightarrowleft<eginmatrixcos5x=0\cos2x=0\cosx=0endmatrix ight.) (Leftrightarrowleft<eginmatrixx=fracpi10+frackpi5\x=fracpi4+frackpi2\x=fracpi2+kpiendmatrix ight.)
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giải các pt
a) (sin^3x.cosx-sinx.cos^3x=fracsqrt28)
b) (sin^3x-cos^24x=sin^25x-cos^26x)
c) (left(2sinx-cosx+1 ight)left(1+cosx ight)=sin^2x)
d) (sin7x+sin9x=2left
Lớp 11 Toán thù Chương 1: HÀM SỐ LƯỢNG GIÁC. PHƯƠNG TRÌNH LƯỢNG GI...
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a/
(Leftrightarrow sinx.cosxleft(sin^2x-cos^2x ight)=fracsqrt28)
(Leftrightarrow2sinx.cosxleft(cos^2x-sin^2x ight)=-fracsqrt24)
(Leftrightarrow sin2x.cos2x=-fracsqrt24)
(Leftrightarrowfrac12sin4x=-fracsqrt24)
(Leftrightarrow sin4x=-fracsqrt22)
(Rightarrowleft<eginmatrix4x=-fracpi4+k2pi\4x=frac5pi4+k2piendmatrix ight.)
(Rightarrowleft<eginmatrixx=-fracpi16+frackpi2\x=frac5pi16+frackpi2endmatrix ight.)
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b/
Câu này đề hơi kì quặc, chúng ta coi lại đề được ko? Biến đổi mấy giải pháp vẫn thấy ko ổn
c/
(Leftrightarrowleft(2sinx-cosx+1 ight)left(1+cosx ight)=1-cos^2x)
(Leftrightarrowleft(2sinx-cosx+1 ight)left(1+cosx ight)=left(1-cosx ight)left(1+cosx ight))
(Leftrightarrowleft<eginmatrix1+cosx=0left(1 ight)\2sinx-cosx+1=1-cosxleft(2 ight)endmatrix ight.)
(left(1 ight)Leftrightarrow cosx=-1Leftrightarrowpi x=pi+k2pi)
(left(2 ight)Leftrightarrow2sinx=0Rightarrow sinx=0)
(Rightarrow x=kpi)
Kết hòa hợp lại ta được (x=kpi)
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d/
(Leftrightarrow2sin8x.cosx=cosleft(fracpi2-2x ight)+1-1-cosleft(fracpi2+4x ight)) (hạ bậc vế phải)
(Leftrightarrow2sin8x.cosx=sin2x+sin4x)
(Leftrightarrow2sin8x.cosx=2sin3x.cosx)
(Leftrightarrow cosxleft(sin8x-sin3x ight)=0)
(Leftrightarrowleft<eginmatrixcosx=0\sin8x=sin3xendmatrix ight.)
(Rightarrowleft<eginmatrixx=fracpi2+kpi\8x=3x+k2pi\8x=pi-3x+k2piendmatrix ight.)
(Rightarrowleft<eginmatrixx=fracpi2+kpi\x=frack2pi5\x=fracpi11+frack2pi11endmatrix ight.)
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Giải các PT sau
1.(cos^2left(x-30^cdot ight)-sin^2left(x-30^cdot ight)=sinleft(x+60^cdot ight))
2.(sin^22x+cos^23x=1)
3.(sin x+sin2x+sin3x+sin4x=0)
4.(sin^2x+sin^22x=sin^23x)
Lớp 11 Tân oán
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1.Pt(Leftrightarrow cosleft(2x-dfracpi3 ight)=sinleft(x+dfracpi3 ight))
(Leftrightarrow cosleft(2x-dfracpi3 ight)=cosleft(dfracpi6-x ight))
(Leftrightarrowleft<eginmatrix2x-dfracpi3=dfracpi6-x+k2pi\2x-dfracpi3=x-dfracpi6+k2piendmatrix ight.)(left(kin Z ight))
(Leftrightarrowleft<eginmatrixx=dfracpi6+dfrack2pi3\x=dfracpi6+k2piendmatrix ight.)(left(kin Z ight))
(Rightarrow x=dfracpi6+dfrack2pi3)(left(kin Z ight))
2.(sin^22x+cos^23x=1)
(Leftrightarrowdfrac1-cos4x2+dfrac1+cos6x2=1)
(Leftrightarrow cos6x=cos4x)
(Leftrightarrowleft<eginmatrixx=kpi\x=dfrackpi5endmatrix ight.)(left(kin Z ight))(Rightarrow x=dfrackpi5)(left(kin Z ight))(Gộp nghiệm)
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3.(PtLeftrightarrowleft(sinx+sin3x ight)+left(sin2x+sin4x ight)=0)
(Leftrightarrow2.sin2x.cosx+2.sin3x.cosx=0)
(Leftrightarrow2cosxleft(sin2x+sin3x ight)=0)
(Leftrightarrowleft<eginmatrixcosx=0\sin3x=-sin2xendmatrix ight.)(Leftrightarrowleft<eginmatrixx=dfracpi2+kpi\sin3x=sinleft(pi+2x ight)endmatrix ight.)((kin Z))
(Leftrightarrowleft<eginmatrixx=dfracpi2+kpi\x=pi+k2pi\x=dfrack2pi5endmatrix ight.)((kin Z))(Rightarrowleft<eginmatrixx=dfracpi2+kpi\x=dfrack2pi5endmatrix ight.)((kin Z))
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4. Pt(Leftrightarrowdfrac1-cos2x2+dfrac1-cos4x2=dfrac1-cos6x2)
