\(\cos^3x-4\sin^3x-3\cos x\sin^2x+\sin x=0\)
Những câu hỏi liên quan
\(4\sin^3x+3\cos^3x-3\sin x-\sin^2x\cos x=0\)
Nhận thấy \(cosx=0\) ko phải nghiệm, chia 2 vế cho \(cos^3x\)
\(4tan^3x+3-3tanx\left(1+tan^2x\right)-tan^2x=0\)
\(\Leftrightarrow tan^3x-tan^2x-3tanx+3=0\)
\(\Leftrightarrow\left(tanx-1\right)\left(tan^2x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=1\\tanx=\sqrt{3}\\tanx=-\sqrt{3}\end{matrix}\right.\) \(\Leftrightarrow...\)
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Cho \(\sin x+\cos x=m\). Tính theo m các biểu thức sau:
1) \(A=\sin^2x+\cos^2x\)
2) \(B=\sin^3x+\cos^3x\)
3) \(C=\sin^4x+\cos^4x\)
4) \(D=\sin^6x+\cos^6x\)
\(sinx+cosx=m\Leftrightarrow\left(sinx+cosx\right)^2=m^2\)
\(\Leftrightarrow1+2sinx.cosx=m^2\Rightarrow sinx.cosx=\dfrac{m^2-1}{2}\)
\(A=sin^2x+cos^2x=1\)
\(B=sin^3x+cos^3x=\left(sinx+cosx\right)^3-3sinx.cosx\left(sinx+cosx\right)\)
\(=m^3-\dfrac{3m\left(m^2-1\right)}{2}=\dfrac{2m^3-3m^3+3m}{2}=\dfrac{3m-m^3}{2}\)
\(C=\left(sin^2+cos^2x\right)^2-2\left(sinx.cosx\right)^2=1-2\left(\dfrac{m^2-1}{2}\right)^2\)
\(D=\left(sin^2x\right)^3+\left(cos^2x\right)^3=\left(sin^2x+cos^2x\right)^3-3\left(sin^2x+cos^2x\right)\left(sinx.cosx\right)^2\)
\(=1-3\left(\dfrac{m^2-1}{2}\right)^2\)
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Giải các phương trình sau:
1) sin2x + sin23x - 3cos22x = 0
2) sin22x + sin24x = sin26x
3) cos4x - 5sin4x = 1
4) sin24x + sin23x = cos22x +cos2x với x∈(0;π)
5) 4sin3x - 1 = 3 - √3cos3x
6)sin2x = cos22x + cos23x
7 tháng 10 2020 lúc 17:01
Giải các phương trình sau:
1) tan x + tan 2x + tan 3x = 0
2) cos 2x. cos 4x = \(\frac{\text{1}}{\text{2}}\)
3) cot x - tan x = cos x - sin x
4) 4sin x. sin 2x. sin 4x = sin 3x
a. ĐKXĐ: ...
\(\frac{sinx}{cosx}+\frac{sin2x}{cos2x}+\frac{sin3x}{cos3x}=0\)
\(\Leftrightarrow\frac{sin2x.cosx+cos2x.sinx}{cosx.cos2x}+\frac{sin3x}{cos3x}=0\)
\(\Leftrightarrow\frac{sin3x}{cosx.cos2x}+\frac{sin3x}{cos3x}=0\)
\(\Leftrightarrow sin3x\left(\frac{cosx.cos2x+cos3x}{cosx.cos2x.cos3x}\right)=0\)
\(\Leftrightarrow sin3x\left(\frac{cosx\left(2cos^2x-1\right)+4cos^3x-3cosx}{cosx.cos2x.cos3x}\right)=0\)
\(\Leftrightarrow sin3x\left(\frac{6cos^2x-4}{cos2x.cos3x}\right)=0\)
\(\Leftrightarrow sin3x\left(\frac{3cos2x-1}{cos2x.cos3x}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin3x=0\\cos2x=\frac{1}{3}\end{matrix}\right.\)
b.
\(cos2x\left(2cos^22x-1\right)=\frac{1}{2}\)
\(\Leftrightarrow4cos^32x-2cos2x-1=0\)
Pt bậc 3 này ko giải được, chắc bạn ghi nhầm đề
c. ĐKXĐ: ...
\(\frac{cosx}{sinx}-\frac{sinx}{cosx}=cosx-sinx\)
\(\Leftrightarrow\frac{\left(cosx-sinx\right)\left(cosx+sinx\right)}{sinx.cosx}=cosx-sinx\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx-sinx=0\Rightarrow x=...\\\frac{cosx+sinx}{sinx.cosx}=1\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow cosx+sinx=sinx.cosx\)
Đặt \(sinx+cosx=t\Rightarrow\left\{{}\begin{matrix}\left|t\right|\le\sqrt{2}\\sinx.cosx=\frac{t^2-1}{2}\end{matrix}\right.\)
\(\Rightarrow t=\frac{t^2-1}{2}\Rightarrow t^2-2t-1=0\Rightarrow\left[{}\begin{matrix}t=1+\sqrt{2}\left(l\right)\\t=1-\sqrt{2}\end{matrix}\right.\)
\(\Rightarrow\sqrt{2}sin\left(x+\frac{\pi}{4}\right)=1-\sqrt{2}\Rightarrow sin\left(x+\frac{\pi}{4}\right)=\frac{1-\sqrt{2}}{\sqrt{2}}\Rightarrow x=...\)
d.
\(\Leftrightarrow2\left(cosx-cos3x\right)sin4x=sin3x\)
\(\Leftrightarrow2sin4x.cosx-2sin4x.cos3x=sin3x\)
\(\Leftrightarrow sin5x+sin3x-sin7x-sinx=sin3x\)
\(\Leftrightarrow sin5x-sin7x-sinx=0\)
\(\Leftrightarrow-2cos6x.sinx-sinx=0\)
\(\Leftrightarrow sinx\left(2cos6x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\\cos6x=-\frac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow...\)
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\(\text{2}\sin^3x-3\sin^{\text{2}}x\cos x+4\sin x\cos^{\text{2}}x-\sin x\cos x+6\cos^3x=7\)
4 tháng 10 2020 lúc 14:50
Giải các phương trình sau
1) sin3x = 0
2) cos25x = 0
3) tan (x - 15o) = 3tan (x + 15o)
4) cos x + cos 2x + cos 3x = 0
5) sin 2x + sin 4x + sin 6x = 0
6) tan x + tan 2x + tan x.tan 2x = 1
7) tan x + tan 2x + tan 3x = tan x.tan 2x.tan 3x
8) cot2x + \(\frac{\text{3}}{\text{sin x}}\) + 3 = 0
1.
\(\Leftrightarrow3x=k\pi\Leftrightarrow x=\frac{k\pi}{3}\)
2.
\(\Leftrightarrow cos5x=0\Leftrightarrow5x=\frac{\pi}{2}+k\pi\Leftrightarrow x=\frac{\pi}{10}+\frac{k\pi}{5}\)
4.
\(cos3x+cosx+cos2x=0\)
\(\Leftrightarrow2cos2x.cosx+cos2x=0\)
\(\Leftrightarrow cos2x\left(2cosx+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos2x=0\\cosx=-\frac{1}{2}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{4}+\frac{k\pi}{2}\\x=\pm\frac{2\pi}{3}+k2\pi\end{matrix}\right.\)
3. ĐKXĐ: ...
\(\Leftrightarrow\frac{sin\left(x-15\right)}{cos\left(x-15\right)}=\frac{3sin\left(x+15\right)}{cos\left(x+15\right)}\)
\(\Leftrightarrow sin\left(x-15\right)cos\left(x+15\right)=3sin\left(x+15\right)cos\left(x-15\right)\)
\(\Leftrightarrow sin2x-sin30^0=3\left[sin2x+sin30^0\right]\)
\(\Leftrightarrow sin2x-\frac{1}{2}=3sin2x+\frac{3}{2}\)
\(\Leftrightarrow sin2x=-1\)
\(\Leftrightarrow2x=-\frac{\pi}{2}+k2\pi\)
\(\Leftrightarrow x=-\frac{\pi}{4}+k\pi\)
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5.
\(sin6x+sin2x+sin4x=0\)
\(\Leftrightarrow2sin4x.cos2x+sin4x=0\)
\(\Leftrightarrow sin4x\left(2cos2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin4x=0\\cos2x=-\frac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{k\pi}{4}\\x=\pm\frac{\pi}{3}+k\pi\end{matrix}\right.\)
6. ĐKXĐ; ...
\(\Leftrightarrow tanx+tan2x=1-tanx.tan2x\)
\(\Leftrightarrow\frac{tanx+tan2x}{1-tanx.tan2x}=1\)
\(\Leftrightarrow tan3x=1\)
\(\Leftrightarrow x=\frac{\pi}{12}+\frac{k\pi}{3}\)
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Giải phương trình lượng giác sau
1) 2 cos 2x -sqrt{3} 0
2)sqrt{3} tan x + 1 0
3) 2 cos2x 1
4) 6 sin2 x- 13 sin x + 5 0
5) 5 cos 2x + 6 cos x + 1 0
6 ) 2 cos 2 2x - 3 cos 2x + 1 0
7) tan 2 x + ( 1 - sqrt{3}) tan x - sqrt{3} 0
8) cos 6x + 2 sin 3x + 3 0
9) cos 2x - 4 cos x - 5 0
10 ) 3 cos 2 x 2 sin 2 x + 4 sin x
11) cos 2x + sin2x + 2 cos x + 1 0
12) cos 4x + sin 4x + sin 2x dfrac{5}{2}
Đọc tiếp
Giải phương trình lượng giác sau
1) 2 cos 2x -\(\sqrt{3}\) = 0
2)\(\sqrt{3}\) tan x + 1 = 0
3) 2 cos2x = 1
4) 6 sin2 x- 13 sin x + 5 = 0
5) 5 cos 2x + 6 cos x + 1 = 0
6 ) 2 cos 2 2x - 3 cos 2x + 1 = 0
7) tan 2 x + ( 1 - \(\sqrt{3}\)) tan x - \(\sqrt{3}\) = 0
8) cos 6x + 2 sin 3x + 3 = 0
9) cos 2x - 4 cos x - 5 = 0
10 ) 3 cos 2 x = 2 sin 2 x + 4 sin x
11) cos 2x + sin2x + 2 cos x + 1 = 0
12) cos 4x + sin 4x + sin 2x = \(\dfrac{5}{2}\)
Giải PT
a) 4sin (3x + \(\frac{\pi}{3}\)) - 2 = 0
b) 4sin ( 4x + 1) -1 = 0
c) sin ( x + \(\frac{x}{4}\)) -1 = 0
d) 2sin ( 2x + 70o) + 1 = 0
e) sin x . cos ( 2x - 3 ) = 0
f) cos 2x -cos 4x = 0
g) cos ( sin 3x) = 1
a)
\(4\sin (3x+\frac{\pi}{3})-2=0\Leftrightarrow \sin (3x+\frac{\pi}{3})=\frac{1}{2}=\sin (\frac{\pi}{6})\)
\(\Rightarrow \left[\begin{matrix} 3x+\frac{\pi}{3}=\frac{\pi}{6}+2k\pi \\ 3x+\frac{\pi}{3}=\pi-\frac{\pi}{6}+2k\pi\end{matrix}\right.\)
\(\Leftrightarrow \left[\begin{matrix} x=\frac{-\pi}{18}+\frac{2\pi}{3}\\ x=\frac{\pi}{6}+\frac{2\pi}{3}\end{matrix}\right.\) (k nguyên)
c)
\(\sin (x+\frac{x}{4})-1=0\Leftrightarrow \sin (\frac{5}{4}x)=1=\sin (\frac{\pi}{2})\)
\(\Rightarrow \frac{5}{4}x=\frac{\pi}{2}+2k\pi\Rightarrow x=\frac{2}{5}\pi+\frac{8}{5}k\pi \) (k nguyên)
d)
\(2\sin (2x+70^0)+1=0\Leftrightarrow \sin (2x+\frac{7}{18}\pi)=-\frac{1}{2}=\sin (\frac{-\pi}{6})\)
\(\Rightarrow \left[\begin{matrix} 2x+\frac{7}{18}\pi=\frac{-\pi}{6}+2k\pi\\ 2x+\frac{7}{18}\pi=\frac{7}{6}\pi+2k\pi\end{matrix}\right.\)
\(\Leftrightarrow \left[\begin{matrix} x=\frac{-5\pi}{18}+k\pi\\ x=\frac{7}{18}\pi+k\pi\end{matrix}\right.\)
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f)
\(\cos 2x-\cos 4x=0\)
\(\Leftrightarrow \cos 2x=\cos 4x\Rightarrow \left[\begin{matrix} 4x=2x+2k\pi\\ 4x=-2x+2k\pi\end{matrix}\right.\)
\(\Rightarrow \left[\begin{matrix} x=k\pi\\ x=\frac{k}{3}\pi \end{matrix}\right.\) ( k nguyên)
b,e,g bạn xem lại đề, đơn vị không thống nhất.
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cos^4x+sin^x+cos(x-pi/4)sin(3x-pi/4)-3/2=0
\(\Leftrightarrow cos^4x+sin^4x+\dfrac{1}{2}\left[sin\left(3x-\dfrac{pi}{4}+x-\dfrac{pi}{4}\right)+sin\left(3x-\dfrac{pi}{4}-x+\dfrac{pi}{4}\right)\right]-\dfrac{3}{2}=0\)
\(\Leftrightarrow1-\dfrac{1}{2}sin^22x+\dfrac{1}{2}\left[sin\left(4x-\dfrac{pi}{2}\right)+sin2x\right]-\dfrac{3}{2}=0\)
=>\(-\dfrac{1}{2}sin^22x-\dfrac{1}{2}+\dfrac{1}{2}\left[-sin\left(\dfrac{pi}{2}-4x\right)+sin2x\right]=0\)
=>\(-sin^22x-1-cos4x+sin2x=0\)
=>\(-sin^22x-1-\left(1-2sin^22x\right)+sin2x=0\)
=>\(-sin^22x-1-1+2sin^22x+sin2x=0\)
=>\(sin^22x+sin2x-2=0\)
=>sin2x-1=0
=>sin2x=1
=>2x=pi/2+k2pi
=>x=pi/4+kpi
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