Bài 4: Ôn tập chương Hàm số lượng giác và phương trình lượng giác
Các câu hỏi tương tự
31 tháng 10 2023 lúc 20:08
\(sinx+4cosx=2+sin2x\)
\(\left(1-sin2x\right)\left(sinx+cosx\right)=cos2x\)
\(1+sinx+cosx+sin2x+cos2x=0\)
\(sinx+sin2x+sin3x=1+cosx+cos2x\)
\(sin^22x-cos^28x=sin\left(\dfrac{17\pi}{2}+10x\right)\)
18 tháng 8 2020 lúc 1:26
giải các pt
a) \(\left(1+tanx\right)sin^2x=3sinx\left(cosx-sinx\right)+3\)
b) \(6sinx-2cos^3x=\frac{5sin4x.sinx}{2cos2x}\)
c) \(cos^3x=2sinx.sin\left(\frac{\pi}{3}-x\right).sin\left(x+\frac{\pi}{3}\right)\)
d) \(cos2x\left(sinx+cosx\right)-4cos^3x\left(1+sin2x\right)=0\)
Giải các phương trình :
1) frac{sin^4x+cos^4x}{sin2x}frac{1}{2}left(tan x+cot2xright)
2) frac{1}{sin x}+frac{1}{sinleft(x-frac{3pi}{2}right)}4sinleft(frac{7pi}{4}-xright)
3)2left(cos^42x-sin^42xright)+cos8x-cos4x0
4)frac{sin^4x+cos^4x}{5sin2x}frac{1}{2}cot2x-frac{1}{8sin2x}
5)sin^4x+cos^4x-3sin2x+frac{5}{2}sin^22x0
Đọc tiếp
Giải các phương trình :
1) \(\frac{\sin^4x+\cos^4x}{\sin2x}=\frac{1}{2}\left(\tan x+\cot2x\right)\)
2) \(\frac{1}{\sin x}+\frac{1}{\sin\left(x-\frac{3\pi}{2}\right)}=4\sin\left(\frac{7\pi}{4}-x\right)\)
3)\(2\left(\cos^42x-\sin^42x\right)+\cos8x-\cos4x=0\)
4)\(\frac{\sin^4x+\cos^4x}{5\sin2x}=\frac{1}{2}\cot2x-\frac{1}{8\sin2x}\)
5)\(\sin^4x+\cos^4x-3\sin2x+\frac{5}{2}\sin^22x=0\)
Giải phương trình:
1, \(2\tan^2x-3\tan x+2\cot^2x-3\cot x+2=0\)
2, \(\cos^23x.\cos2x-\cos^2x=0\)
3, \(\cos^22x-2\left(\cos x+\sin x\right)^2-3\sin2x+1=0\)
4, \(1-\frac{1}{\tan x}=\frac{1}{2\tan2x}\)
Mọi người giúp mình với ạ!!! Mình cảm ơn nhiều!!!
18 tháng 8 2020 lúc 1:20
giải các pt
a) \(1-2cos2x-\sqrt{3}sinx+cosx=0\)
b) \(cos2x+cos^2x-sinx.cosx=8\left(cosx-sinx\right)\)
c) \(sin^2x+3sinx.cosx-4cos^2x=4\left(sinx-cosx\right)\)
d) \(\frac{cos^3x-sin^3x}{2cosx+3sinx}=cos2x\)
1) 4cos^24x+2left(sqrt{3}+sqrt{2}right)cos4x+sqrt{6}0
2) cos4x+2+sinleft(2x+frac{3pi}{2}right)2cos^2x
3) sinleft(x+frac{pi}{3}right)+sqrt{3}sinleft(frac{pi}{6}-xright)1
4) 2cosleft(4x-frac{pi}{3}right)+4cos2x-1
5) cos^22x+cos^23xsin^2x
6) sinx+left(sqrt{2}-1right)cosx1
7) cos2x-left(sqrt{3}+1right)cosx+frac{2+sqrt{3}}{2}0
Đọc tiếp
1) \(4cos^24x+2\left(\sqrt{3}+\sqrt{2}\right)cos4x+\sqrt{6}=0\)
2) \(cos4x+2+sin\left(2x+\frac{3\pi}{2}\right)=2cos^2x\)
3) \(sin\left(x+\frac{\pi}{3}\right)+\sqrt{3}sin\left(\frac{\pi}{6}-x\right)=1\)
4) \(2cos\left(4x-\frac{\pi}{3}\right)+4cos2x=-1\)
5) \(cos^22x+cos^23x=sin^2x\)
6) \(sinx+\left(\sqrt{2}-1\right)cosx=1\)
7) \(cos2x-\left(\sqrt{3}+1\right)cosx+\frac{2+\sqrt{3}}{2}=0\)
1)cos2x+52sqrt{2}left(2-cosxright)sinleft(x-frac{pi}{4}right)
2)
sin^2x-2sinx+2sin^23x
3)
sinx-2sin2x-sin3x2sqrt{2}
4)
left(cos4x-cos2xright)^25+sin3x
5)
sqrt{5+sin^23xsinx+2cosx}
6)
5left(sinx+frac{cos3x+sin3x}{1+2sin2x}right)cos2x+3
7)
frac{sin^42x+cos^42x}{tanleft(frac{pi}{4}-xright)tanleft(frac{pi}{4}+xright)}cos^44x
Đọc tiếp
1)\(cos2x+5=2\sqrt{2}\left(2-cosx\right)sin\left(x-\frac{\pi}{4}\right)\)
2)
\(sin^2x-2sinx+2=sin^23x\)
3)
\(sinx-2sin2x-sin3x=2\sqrt{2}\)
4)
\(\left(cos4x-cos2x\right)^2=5+sin3x\)
5)
\(\sqrt{5+sin^23x=sinx+2cosx}\)
6)
\(5\left(sinx+\frac{cos3x+sin3x}{1+2sin2x}\right)=cos2x+3\)
7)
\(\frac{sin^42x+cos^42x}{tan\left(\frac{\pi}{4}-x\right)tan\left(\frac{\pi}{4}+x\right)}=cos^44x\)
1) sin^2left(frac{x}{2}-frac{pi}{4}right).tan^2x-cos^2frac{x}{2}0
2) tanxsin^2xleft(c-frac{pi}{2010}right)+cos^2left(2x+frac{pi}{2010}right)+sinx.sinleft(3x+frac{pi}{1005}right)
3) 1+2cosxleft(sinx-1right)+sqrt{2}sinx+4cosx.sin^2frac{x}{2}0
4) 3cos4x-8cos^6x+2cos4x3
5) 1+sinx.sin2x-cosx.sin^22x2cos^2left(frac{pi}{4}-xright)
6) sinx.sin4xsqrt{2}cosleft(frac{pi}{6}-xright)-4sqrt{3}cos^2x.sinx.cos2x
7) frac{tan^2x+tanx}{tan^2x+1}frac{sqrt{2}}{2}sinleft(x+frac{pi}{4}right)
8) cos^4x+sin^4x+co...
Đọc tiếp
1) \(sin^2\left(\frac{x}{2}-\frac{\pi}{4}\right).tan^2x-cos^2\frac{x}{2}=0\)
2) \(tanx=sin^2x\left(c-\frac{\pi}{2010}\right)+cos^2\left(2x+\frac{\pi}{2010}\right)+sinx.sin\left(3x+\frac{\pi}{1005}\right)\)
3) \(1+2cosx\left(sinx-1\right)+\sqrt{2}sinx+4cosx.sin^2\frac{x}{2}=0\)
4) \(3cos4x-8cos^6x+2cos4x=3\)
5) \(1+sinx.sin2x-cosx.sin^22x=2cos^2\left(\frac{\pi}{4}-x\right)\)
6) \(sinx.sin4x=\sqrt{2}cos\left(\frac{\pi}{6}-x\right)-4\sqrt{3}cos^2x.sinx.cos2x\)
7) \(\frac{tan^2x+tanx}{tan^2x+1}=\frac{\sqrt{2}}{2}sin\left(x+\frac{\pi}{4}\right)\)
8) \(cos^4x+sin^4x+cos\left(x-\frac{\pi}{4}\right).sin\left(3x-\frac{\pi}{4}\right)-\frac{3}{2}=0\)
giải phương trình sau:
a,frac{sin2x+2cosx-sinx-1}{tanx+sqrt{3}}0
b,frac{left(1+sinx+cos2xright)sinxleft(x+frac{pi}{4}right)}{1+tanx}frac{1}{sqrt{2}}cosx
c,frac{left(1-sin2xright)cosx}{left(1+sin2xright)left(1-sinxright)}sqrt{3}
d,frac{1}{sinx}+frac{1}{sinleft(x-frac{3pi}{2}right)}4sinleft(frac{7pi}{4}-xright)
Đọc tiếp
giải phương trình sau:
a,\(\frac{sin2x+2cosx-sinx-1}{tanx+\sqrt{3}}=0\)
b,\(\frac{\left(1+sinx+cos2x\right)sinx\left(x+\frac{\pi}{4}\right)}{1+tanx}=\frac{1}{\sqrt{2}}cosx\)
c,\(\frac{\left(1-sin2x\right)cosx}{\left(1+sin2x\right)\left(1-sinx\right)}=\sqrt{3}\)
d,\(\frac{1}{sinx}+\frac{1}{sin\left(x-\frac{3\pi}{2}\right)}=4sin\left(\frac{7\pi}{4}-x\right)\)