cho tanx=2 tính Q=\(\dfrac{\sin^3x}{2\sin x+\cos^3x}\)
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Cho tanx= 3, tính A =\(\frac{sin^3x-cos^3x}{sin^3x+cos^3x}\)
Cho hàm số \(y=\dfrac{xsinx+cosx}{tanx}\). CMR: y' + y tanx = -\(\dfrac{cos^3x}{sin^2x}\)
\(y=\dfrac{xsinx}{tanx}+\dfrac{cosx}{tanx}=x.cosx+\dfrac{cos^2x}{sinx}=x.cosx+\dfrac{1}{sinx}-sinx\)
\(y'=cosx-x.sinx-\dfrac{cosx}{sin^2x}-cosx=-x.sinx-\dfrac{cosx}{sin^2x}\)
\(\Rightarrow y'+y.tan=-x.sinx-\dfrac{cosx}{sin^2x}+x.sinx+cosx\)
\(=cosx\left(1-\dfrac{1}{sin^2x}\right)=\dfrac{-cosx\left(1-sin^2x\right)}{sin^2x}=\dfrac{-cos^3x}{sin^2x}\)
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a/sin3x+cos2x1+2sin xcos2xb/sin^3x+cos^3x2left(sin^5x+cos^5xright)c/dfrac{tan x}{sin x}-dfrac{sin x}{cos x}dfrac{sqrt{2}}{2}d/dfrac{cos xleft(cos x+2sin xright)+3sin xleft(sin x+sqrt{2}right)}{sin2x-1}1e/sin^2x+sin^23x-2cos^22x0f/dfrac{tan x-sin x}{sin^3x}dfrac{1}{cos x}g/sin2xleft(cos x+tan2xright)4cos^2xh/sin^2x+sin^23xcos^2x+cos^23xk/4sin2xdfrac{cos^2x-sin^2x}{cos^6x+sin^6x}mọi người giải giúp em với em đang cần gấp ạ
Đọc tiếp
a/\(\sin3x+\cos2x=1+2\sin x\cos2x\)
b/\(\sin^3x+\cos^3x=2\left(\sin^5x+\cos^5x\right)\)
c/\(\dfrac{\tan x}{\sin x}-\dfrac{\sin x}{\cos x}=\dfrac{\sqrt{2}}{2}\)
d/\(\dfrac{\cos x\left(\cos x+2\sin x\right)+3\sin x\left(\sin x+\sqrt{2}\right)}{\sin2x-1}=1\)
e/\(\sin^2x+\sin^23x-2\cos^22x=0\)
f/\(\dfrac{\tan x-\sin x}{\sin^3x}=\dfrac{1}{\cos x}\)
g/\(\sin2x\left(\cos x+\tan2x\right)=4\cos^2x\)
h/\(\sin^2x+\sin^23x=\cos^2x+\cos^23x\)
k/\(4\sin2x=\dfrac{\cos^2x-\sin^2x}{\cos^6x+\sin^6x}\)
mọi người giải giúp em với em đang cần gấp ạ
JE
18 tháng 8 2020 lúc 1:15
giai cac pt
a) \(sin^3\left(x+\frac{\pi}{4}\right)=\sqrt{2}sinx\)
b) \(cos^3x-sin^3x=\sqrt{2}cos\left(x-\frac{\pi}{4}\right)\)
c) \(\frac{1-tanx}{1+tanx}=1+2sinx\)
d) \(\left(1+tanx\right)sin^2x=3sinx\left(cosx-sinx\right)+3\)
JE
19 tháng 8 2020 lúc 0:53
giai pt
a) \(cos^3x-sin^3x=\sqrt{2}cos\left(x-\frac{\pi}{4}\right)\)
b) \(\frac{1-tanx}{1+tanx}=1+2sinx\)
c) \(\left(1+tanx\right)sin^2x=3sinx\left(cosx-sinx\right)+3\)
a/
\(\Leftrightarrow cos^3x-sin^3x=cosx+sinx\)
- Với \(cosx=0\Rightarrow sinx=-1\Rightarrow x=-\frac{\pi}{2}+k2\pi\) là 1 nghiệm
- Với \(cosx\ne0\) chia 2 vế cho \(cos^3x\)
\(\Leftrightarrow1-tan^3x=\frac{1}{cos^2x}+tanx.\frac{1}{cos^2x}\)
\(\Leftrightarrow1-tan^3x=1+tan^2x+tanx\left(1+tan^2x\right)\)
\(\Leftrightarrow2tan^3x+tan^2x+tanx=0\)
\(\Leftrightarrow tanx\left(2tan^2x+tanx+1\right)=0\)
\(\Leftrightarrow tanx=0\Rightarrow x=k\pi\)
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b/
ĐKXĐ: \(\left\{{}\begin{matrix}x\ne\frac{\pi}{2}+k\pi\\x\ne-\frac{\pi}{4}+k\pi\end{matrix}\right.\)
\(\Leftrightarrow\frac{1-\frac{sinx}{cosx}}{1+\frac{sinx}{cosx}}=1+2sinx\)
\(\Leftrightarrow\frac{cosx-sinx}{cosx+sinx}=1+2sinx\)
\(\Leftrightarrow cosx-sinx=\left(1+2sinx\right)\left(cosx+sinx\right)\)
\(\Leftrightarrow sinx+sinx.cosx+sin^2x=0\)
\(\Leftrightarrow sinx\left(sinx+cosx+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=0\Rightarrow x=k\pi\\sinx+cosx=-1\left(1\right)\end{matrix}\right.\)
\(\left(1\right)\Leftrightarrow\sqrt{2}sin\left(x+\frac{\pi}{4}\right)=-1\)
\(\Leftrightarrow sin\left(x+\frac{\pi}{4}\right)=-\frac{\sqrt{2}}{2}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\frac{\pi}{4}=-\frac{\pi}{4}+k2\pi\\x+\frac{\pi}{4}=\frac{5\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\frac{\pi}{2}+k2\pi\left(l\right)\\x=\pi+k2\pi\end{matrix}\right.\)
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c/
ĐKXĐ: ...
Chia 2 vế cho \(cos^2x\) ta được:
\(\left(1+tanx\right)tan^2x=3tanx\left(1-tanx\right)+3\left(1+tan^2x\right)\)
\(\Leftrightarrow tan^3x+tan^2x=3tanx-3tan^2x+3+3tan^2x\)
\(\Leftrightarrow tan^3x+tan^2x-3tanx-3=0\)
\(\Leftrightarrow\left(tanx+1\right)\left(tan^2x-3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=-1\\tanx=\sqrt{3}\\tanx=-\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-\frac{\pi}{4}+k\pi\\x=\frac{\pi}{3}+k\pi\\x=-\frac{\pi}{3}+k\pi\end{matrix}\right.\)
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Xem thêm câu trả lời
\(\sin^3x\cdot\cos x-\sin x\cdot\cos^3x=\dfrac{\sqrt{2}}{8}\)
cho tanx = -2 tính H = \(\dfrac{sin^3x+5cos^3x}{3sinx-2cosx}\)
tan x=-2
=>sin x/cosx=-2
=>sin x=-2*cosx
\(1+tan^2x=\dfrac{1}{cos^2x}\)
=>\(\dfrac{1}{cos^2x}=1+2=3\)
=>\(cos^2x=\dfrac{1}{3}\)
\(H=\dfrac{sin^3x+5\cdot cos^3x}{3\cdot sinx-2\cdot cosx}\)
\(=\dfrac{\left(-2\cdot cosx\right)^3+5\cdot cos^3x}{3\cdot\left(-2\right)\cdot cosx-2\cdot cosx}\)
\(=\dfrac{-8\cdot cos^3x+5\cdot cos^3x}{-6\cdot cos-2\cdot cosx}=\dfrac{-3\cdot cos^3x}{-8\cdot cosx}=\dfrac{3}{8}\cdot cos^2x\)
=3/8*1/3
=1/8
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B=\(\dfrac{cos^3x+cosx.sin^2x-sin^3x}{sin^3x-cos^3x}\) khi tan x =2
tan x=2
=>\(\dfrac{sinx}{cosx}=2\)
=>\(sinx=2\cdot cosx\)
\(B=\dfrac{cos^3x+cosx\cdot sin^2x-sin^3x}{sin^3x-cos^3x}\)
\(=\dfrac{cos^3x+cosx\cdot4cos^2x-8cos^3x}{8cos^3x-cos^3x}\)
\(=\dfrac{-3cos^3x}{7cos^3x}=-\dfrac{3}{7}\)
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a) 1-cot^4xfrac{2}{sin^2x}-frac{1}{sin^4x}b)frac{1-2sinx.cosx}{cos^2-sin^2}frac{1-tanx}{1+tanx}c)frac{sin^2x}{sinx-cosx}+frac{sinx+cosx}{1-tanx}sinx+cosxd)sqrt{frac{1+cosx}{1-cosx}}-sqrt{frac{1-cosx}{1+cosx}}frac{2.cosx}{|sin|}e)tan^3x+tan^2x+tanx+1frac{sinx+cosx}{cos^3x}
Đọc tiếp
a) \(1-cot^4x=\frac{2}{sin^2x}-\frac{1}{sin^4x}\)
b)\(\frac{1-2sinx.cosx}{cos^2-sin^2}\)\(=\frac{1-tanx}{1+tanx}\)\(\)
c)\(\frac{sin^2x}{sinx-cosx}+\frac{sinx+cosx}{1-tanx}=sinx+cosx\)
d)\(\sqrt{\frac{1+cosx}{1-cosx}}-\sqrt{\frac{1-cosx}{1+cosx}}=\frac{2.cosx}{|sin|}\)
e)\(tan^3x+tan^2x+tanx+1=\frac{sinx+cosx}{cos^3x}\)