\(GPT:2\sqrt{3}.cotx-\frac{1}{sinx}=1+\frac{\sqrt{3}cotx}{sinx}-cot^2x\)
Những câu hỏi liên quan
giải pt \(\sqrt{3}sinx+cosx=3+\dfrac{1}{\sqrt{3}sinx}+cosx+1\)
\(2\sqrt{3}cotx-\dfrac{1}{sinx}=1+\dfrac{\sqrt{3}cotx}{sinx}-cot\)2x
tìm tập xác định của hàm số sau:
a, y=cot \(\left(\frac{\pi}{2}.sinx\right)\)
b, y= \(\sqrt{sinx-1}+2-cos^2x\)
c, y= \(\frac{tanx+cotx}{cos2x}\)
d, y=\(\frac{sinx-tanx}{sinx+cotx}\)
e, y=\(\frac{cotx}{cos^2x-3cosx+2}\)
a/ ĐKXĐ:
\(sin\left(\frac{\pi}{2}.sinx\right)\ne0\Rightarrow\frac{\pi}{2}.sinx\ne k\pi\)
\(\Rightarrow sinx\ne2k\)
Mà \(-1\le sinx\le1\Rightarrow sinx\ne0\Rightarrow x\ne k\pi\)
b/
\(sinx-1\ge0\Leftrightarrow sinx\ge1\Rightarrow sinx=1\)
\(\Rightarrow x=\frac{\pi}{2}+k2\pi\)
c/
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\\cos2x\ne0\end{matrix}\right.\) \(\Rightarrow sin4x\ne0\)
\(\Rightarrow x\ne\frac{k\pi}{4}\)
d/
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\\sinx+cotx\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}sin2x\ne0\\sin^2x+cosx\ne0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x\ne k\pi\\-cos^2x+cosx+1\ne0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x\ne\frac{k\pi}{2}\\cosx\ne\frac{1-\sqrt{5}}{2}\\\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x\ne\frac{k\pi}{2}\\x\ne\pm arccos\left(\frac{1-\sqrt{5}}{2}\right)+k2\pi\end{matrix}\right.\)
e/
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne1\end{matrix}\right.\) \(\Leftrightarrow sinx\ne0\Rightarrow x\ne k\pi\)
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GPT : \(\dfrac{1}{sinx+cot2x}=\dfrac{\sqrt{2}.\left(cosx-sinx\right)}{cotx-1}\)
16 tháng 9 2020 lúc 14:46
GPT
a) \(sinx-cos2x=0\)
b) \(sinx+\sqrt{3}sin\frac{x}{2}=0\)
c) \(sinx-\sqrt{3}cos\frac{x}{2}=0\)
d) \(tan\left(3x-\frac{\pi}{5}\right)=cotx\)
e) \(tan3x.tanx=1\)
a.
\(cos2x=sinx\)
\(\Leftrightarrow cos2x=cos\left(\frac{\pi}{2}-x\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}2x=\frac{\pi}{2}-x+k2\pi\\2x=x-\frac{\pi}{2}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{6}+\frac{k2\pi}{3}\\x=-\frac{\pi}{2}+k2\pi\end{matrix}\right.\)
b.
\(\Leftrightarrow2sin\frac{x}{2}cos\frac{x}{2}+\sqrt{3}sin\frac{x}{2}=0\)
\(\Leftrightarrow sin\frac{x}{2}\left(2cos\frac{x}{2}+\sqrt{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\frac{x}{2}=0\\cos\frac{x}{2}=-\frac{\sqrt{3}}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\frac{x}{2}=k\pi\\\frac{x}{2}=\frac{5\pi}{6}+k2\pi\\\frac{x}{2}=-\frac{5\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\frac{5\pi}{3}+k4\pi\\x=-\frac{5\pi}{3}+k4\pi\end{matrix}\right.\)
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c.
\(\Leftrightarrow2sin\frac{x}{2}cos\frac{x}{2}-\sqrt{3}cos\frac{x}{2}=0\)
\(\Leftrightarrow cos\frac{x}{2}\left(2sin\frac{x}{2}-\sqrt{3}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cos\frac{x}{2}=0\\sin\frac{x}{2}=\frac{\sqrt{3}}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\frac{x}{2}=\frac{\pi}{2}+k\pi\\\frac{x}{2}=\frac{\pi}{3}+k2\pi\\\frac{x}{2}=\frac{2\pi}{3}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\pi+k2\pi\\x=\frac{2\pi}{3}+k4\pi\\x=\frac{4\pi}{3}+k4\pi\end{matrix}\right.\)
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d.
ĐKXĐ: ...
\(\Leftrightarrow tan\left(3x-\frac{\pi}{5}\right)=tan\left(\frac{\pi}{2}-x\right)\)
\(\Leftrightarrow3x-\frac{\pi}{5}=\frac{\pi}{2}-x+k\pi\)
\(\Leftrightarrow x=\frac{7\pi}{40}+\frac{k\pi}{4}\)
e.
ĐKXĐ: \(\left\{{}\begin{matrix}cos3x\ne0\\cosx\ne0\end{matrix}\right.\) \(\Leftrightarrow x\ne\frac{\pi}{6}+\frac{k\pi}{3}\)
\(\frac{sin3x.sinx}{cos3x.cosx}=1\)
\(\Leftrightarrow cos3x.cosx=sin3x.sinx\)
\(\Leftrightarrow cos3x.cosx-sin3x.sinx=0\)
\(\Leftrightarrow cos4x=0\)
\(\Leftrightarrow x=\frac{\pi}{8}+\frac{k\pi}{4}\)
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Tìm tập xác định của hàm số :
1.yfrac{1}{sinx-cosx}
2.yfrac{3}{sin^2x-cos^2x}
3.yfrac{cotx}{cosx-1}
3.yfrac{1-sinx}{sinx+1}
4.yfrac{1-2cosx}{sin3x-sinx}
5.ytanx+cotx
6.yfrac{2x}{1-sin^2x}
7.ytanleft(3x-1right)
8.ysinleft(x-1right)
9.ysqrt{frac{1-sinx}{1+cosx}}
10.ysqrt{sinx+2}
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Tìm tập xác định của hàm số :
1.y=\(\frac{1}{sinx-cosx}\)
2.y=\(\frac{3}{sin^2x-cos^2x}\)
3.y=\(\frac{cotx}{cosx-1}\)
3.y=\(\frac{1-sinx}{sinx+1}\)
4.y=\(\frac{1-2cosx}{sin3x-sinx}\)
5.y=\(tanx+cotx\)
6.y=\(\frac{2x}{1-sin^2x}\)
7.y=\(tan\left(3x-1\right)\)
8.y=\(sin\left(x-1\right)\)
9.y=\(\sqrt{\frac{1-sinx}{1+cosx}}\)
10.y=\(\sqrt{sinx+2}\)
tìm tập xác định của hàm số
1.y=\(cot\left(\dfrac{\pi}{3}-x\right)\)
2.y=\(\dfrac{tan2x-1}{\sqrt{1+sinx}+1}\)
3.y=\(\sqrt{\sqrt{1+sinx}-\sqrt{2}}\)
4.y=\(\dfrac{3cos4x-3}{\sqrt{2-2cosx}-2}\)
5.y=\(\dfrac{1-cot3x}{1-\sqrt{1+sin3x}}\)
6.y=\(cot2x+cotx\)
1. \(sin\left(\dfrac{\pi}{3}-x\right)\ne0\Leftrightarrow\dfrac{\pi}{3}-x\ne k\pi\Leftrightarrow x\ne\dfrac{\pi}{3}-k\pi\)
2. \(cos2x\ne0\Leftrightarrow2x\ne\dfrac{\pi}{2}+k\pi\Leftrightarrow x\ne\dfrac{\pi}{4}+\dfrac{k\pi}{2}\)
3. \(\sqrt{1+sinx}-\sqrt{2}\ge0\Leftrightarrow1+sinx\ge2\Leftrightarrow sinx\ge1\Leftrightarrow sinx=1\Leftrightarrow x=\dfrac{\pi}{2}+k2\pi\)
4. \(\sqrt{2-2cosx}-2\ne0\Leftrightarrow2-2cosx\ne4\Leftrightarrow cosx\ne-1\Leftrightarrow x\ne\pi+k2\pi\)
5. \(1-\sqrt{1+sin3x}\ne0\Leftrightarrow sin3x\ne0\Leftrightarrow3x\ne k\pi\Leftrightarrow x\ne\dfrac{k\pi}{3}\)
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Tìm TXĐ
1. y=\(\frac{cotx}{1-sinx}\)
2.y=\(\frac{1+tan\left(2x+\frac{\pi}{3}\right)}{cot^{2^{ }}x+1}\)
3.y=\(\sqrt{\frac{5-3cos2x}{1+sin\left(2x-\frac{\pi}{2}\right)}}\)
4.y=\(\frac{1+cot\left(x+\frac{\pi}{3}\right)}{tan^2\left(3x-\frac{\pi}{4}\right)}\)
\(\text{1) Đ}K:\left\{{}\begin{matrix}sinx\ne0\\1-sinx\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne m\pi\\x\ne\frac{\pi}{2}+n2\pi\end{matrix}\right.\)
\(2\text{) }ĐK:\left\{{}\begin{matrix}cos\left(2x+\frac{\pi}{3}\right)\ne0\\sinx\ne0\end{matrix}\right.\Leftrightarrow\\ \left\{{}\begin{matrix}2x+\frac{\pi}{3}\ne\frac{\pi}{2}+m\pi\\x\ne n\pi\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{12}+\frac{m\pi}{2}\\x\ne n\pi\end{matrix}\right.\)
\(3\text{) }ĐK:\left\{{}\begin{matrix}\frac{5-3cos2x}{1+sin\left(2x-\frac{\pi}{2}\right)}\ge0\\1+sin\left(2x-\frac{\pi}{2}\right)\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}5-3cos2x\ge0\\sin\left(2x-\frac{\pi}{2}\right)\ne-1\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}cos2x\le\frac{5}{3}\left(T/m\right)\\2x-\frac{\pi}{2}\ne\frac{3\pi}{2}+k2\pi\end{matrix}\right.\Leftrightarrow x\ne\pi+k\pi\)
\(4\text{) }ĐK:\left\{{}\begin{matrix}sin\left(x+\frac{\pi}{3}\right)\ne0\\cos\left(3x-\frac{\pi}{4}\right)\ne0\\tan\left(3x-\frac{\pi}{4}\right)\ne0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x+\frac{\pi}{3}\ne a\pi\\3x-\frac{\pi}{4}\ne\frac{\pi}{2}+b\pi\\3x-\frac{\pi}{4}\ne c\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne-\frac{\pi}{3}+a\pi\\x\ne\frac{\pi}{4}+\frac{b\pi}{3}\\x\ne\frac{\pi}{12}+\frac{c\pi}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x\ne-\frac{\pi}{3}+a\pi\\x\ne\frac{\pi}{12}+\frac{k\pi}{6}\end{matrix}\right.\)
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Tìm tập xác đinh của các hàm số sau
29 , yfrac{tanx+cosx}{sinx}
30 , yfrac{1}{sinx}-frac{1}{cosx}
31 , yfrac{cosx+cotx}{sinx}
32 , yfrac{tanx+cotx}{1-sin2x}
33 , ytanx+frac{1}{cosfrac{x}{2}}
34 , yfrac{1-tanx}{1-cotx}
35 , yfrac{cotx}{cosx-1}
36 , yfrac{3}{sin^2x-cos^2x}
37 , yfrac{2}{cosx-cos3x}
38 , yfrac{sqrt{x}}{sinpi x}
39 , yfrac{2-cosx}{1+tanleft(x-frac{pi}{3}right)}
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Tìm tập xác đinh của các hàm số sau
29 , \(y=\frac{tanx+cosx}{sinx}\)
30 , \(y=\frac{1}{sinx}-\frac{1}{cosx}\)
31 , \(y=\frac{cosx+cotx}{sinx}\)
32 , \(y=\frac{tanx+cotx}{1-sin2x}\)
33 , \(y=tanx+\frac{1}{cos\frac{x}{2}}\)
34 , \(y=\frac{1-tanx}{1-cotx}\)
35 , \(y=\frac{cotx}{cosx-1}\)
36 , \(y=\frac{3}{sin^2x-cos^2x}\)
37 , \(y=\frac{2}{cosx-cos3x}\)
38 , \(y=\frac{\sqrt{x}}{sin\pi x}\)
39 , \(y=\frac{2-cosx}{1+tan\left(x-\frac{\pi}{3}\right)}\)
ĐKXĐ:
29.
\(\left\{{}\begin{matrix}cosx\ne0\\sinx\ne0\end{matrix}\right.\) \(\Leftrightarrow sinx.cosx\ne0\)
\(\Leftrightarrow sin2x\ne0\Leftrightarrow x\ne\frac{k\pi}{2}\)
30.
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\end{matrix}\right.\) \(\Leftrightarrow x\ne\frac{k\pi}{2}\) (như câu trên)
31.
\(sinx\ne0\Leftrightarrow x\ne k\pi\)
32.
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\\sin2x\ne1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}sin2x\ne0\\sin2x\ne1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{k\pi}{2}\\x\ne\frac{\pi}{2}+k2\pi\end{matrix}\right.\)
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33.
\(\left\{{}\begin{matrix}cosx\ne0\\cos\frac{x}{2}\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{\pi}{2}+k\pi\\x\ne\pi+k2\pi\end{matrix}\right.\)
34.
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne0\\cotx\ne1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}sin2x\ne0\\cotx\ne1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{k\pi}{2}\\x\ne\frac{\pi}{4}+k\pi\end{matrix}\right.\)
35.
\(\left\{{}\begin{matrix}sinx\ne0\\cosx\ne1\end{matrix}\right.\) \(\Leftrightarrow sinx\ne0\)
\(\Leftrightarrow x\ne k\pi\)
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36.
\(sin^2x-cos^2x\ne0\Leftrightarrow cos2x\ne0\)
\(\Leftrightarrow x\ne\frac{\pi}{4}+\frac{k\pi}{2}\)
37.
\(cos3x\ne cosx\Leftrightarrow\left\{{}\begin{matrix}3x\ne x+k2\pi\\3x\ne-x+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne k\pi\\x\ne\frac{k\pi}{2}\end{matrix}\right.\) \(\Leftrightarrow x\ne\frac{k\pi}{2}\)
38.
\(\left\{{}\begin{matrix}x\ge0\\sin\pi x\ne0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\\pi x\ne k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x\ne k\end{matrix}\right.\)
39.
\(\left\{{}\begin{matrix}cos\left(x-\frac{\pi}{3}\right)\ne0\\tan\left(x-\frac{\pi}{3}\right)\ne-1\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x-\frac{\pi}{3}\ne\frac{\pi}{2}+k\pi\\x-\frac{\pi}{3}\ne-\frac{\pi}{4}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\ne\frac{5\pi}{6}+k\pi\\x\ne-\frac{\pi}{12}+k\pi\end{matrix}\right.\)
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giải hộ mình với : chứng minh\(\left(\frac{sinx+cotx}{1+sinx.tanx}\right)^2=\frac{sin^2x+cot^2x}{1+sin^2x.tan^2x}\)