x x 90 = 180
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1: 90<x<180
=>cosx<0
=>\(cosx=-\sqrt{1-\left(\dfrac{4}{5}\right)^2}=-\dfrac{3}{5}\)
\(sin2x=2\cdot sinx\cdot cosx=2\cdot\dfrac{4}{5}\cdot\dfrac{-3}{5}=\dfrac{-24}{25}\)
\(cos2x=2\cdot cos^2x-1=2\cdot\dfrac{9}{25}-1=-\dfrac{7}{25}\)
\(tan2x=\dfrac{-24}{25}:\dfrac{-7}{25}=\dfrac{24}{7}\)
2: 0<x<90
=>cosx>0
=>\(cosx=\sqrt{1-\left(\dfrac{1}{2}\right)^2}=\dfrac{\sqrt{3}}{2}\)
\(cos2x=2\cdot cos^2x-1=2\cdot\dfrac{3}{4}-1=\dfrac{6}{4}-1=\dfrac{2}{4}=\dfrac{1}{2}\)
90 độ<x<180 độ
=>cosx<0
=>\(cosx=-\sqrt{1-\left(\dfrac{12}{13}\right)^2}=-\dfrac{5}{13}\)
\(tanx=\dfrac{12}{13}:\dfrac{-5}{13}=-\dfrac{12}{5}\)
\(E=\dfrac{6\cdot\dfrac{-12}{5}+\dfrac{12}{13}}{2\cdot\dfrac{-5}{13}+\dfrac{5}{12}}=\dfrac{-\dfrac{72}{5}+\dfrac{12}{13}}{-\dfrac{10}{13}+\dfrac{5}{12}}=\dfrac{10512}{275}\)
\(\Leftrightarrow3sin^2x-2sinx.cosx-5cos^2x=0\)
Nhận thấy \(cosx=0\) ko phải nghiệm, chia 2 vế cho \(cos^2x\)
\(3tan^2x-2tanx-5=0\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=-1\\tanx=\frac{5}{3}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-45^0+k180^0\\x=arctan\left(\frac{5}{3}\right)+k180^0\end{matrix}\right.\)
X= 200 - 300 = -100
X= 900 + 400 = 1300
X= 180 : 90 = 2
X= 240 : 60 = 4
Tìm x :
x + 300 = 200
x = 200 - 300
x = -100
x - 400 = 900
x = 900 + 400
x = 1300
X x 90 = 180
X = 180 : 90
X = 2
240 : x = 60
x = 240 : 60
x = 4
1) \(x+y=10\) mà \(x=y\) nên: \(x=y=\dfrac{10}{2}=5\)
2) \(2x+3y=180\) mà \(x=y\)
Ta có: \(2y+3y=180\Rightarrow5y=180\Rightarrow y=180:5=36\)
Vậy \(x=y=36\)
3) \(x+y=180\) mà \(x=y\) nên: \(x=y=\dfrac{180}{2}=90\)
4) \(3x+5y=13\) mà \(y=2x\) ta có:
\(3x+5\cdot2x=13\Rightarrow13x=13\Rightarrow x=1\)
\(y=2x=2\cdot1=2\)
Các câu còn lại bạn làm tương tự
1.
\(\Leftrightarrow2sinx.cosx+2cosx=0\)
\(\Leftrightarrow2cosx\left(sinx+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\sinx=-1\end{matrix}\right.\)
\(\Leftrightarrow cosx=0\) (do \(cosx=0\Leftrightarrow sinx=\pm1\) bao hàm luôn cả pt \(sinx=-1\))
\(\Leftrightarrow x=\dfrac{\pi}{2}+k\pi\)
2.
\(\Leftrightarrow\left[{}\begin{matrix}2x-10^0=60^0+k360^0\\2x-10^0=120^0+n360^0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=35^0+k180^0\\x=65^0+n180^0\end{matrix}\right.\)
Do \(-120^0< x< 90^0\Rightarrow\left\{{}\begin{matrix}-120^0< 35^0+k180^0< 90^0\\-120^0< 65^0+n180^0< 90^0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}k=0\\n=\left\{-1;0\right\}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=35^0\\x=-115^0\\x=65^0\end{matrix}\right.\)
3. Làm tương tự câu 2
4.
\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{2}cos\left(10x+\dfrac{4\pi}{5}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2}cos\left(\dfrac{x}{2}-2\pi\right)\right)=0\)
\(\Leftrightarrow cos\left(10x+\dfrac{4\pi}{5}\right)+cos\left(\dfrac{x}{2}-2\pi\right)=0\)
\(\Leftrightarrow cos\left(10x+\dfrac{4\pi}{5}\right)+cos\left(\dfrac{x}{2}\right)=0\)
\(\Leftrightarrow cos\left(10x+\dfrac{4\pi}{5}\right)=-cos\left(\dfrac{x}{2}\right)=cos\left(\pi-\dfrac{x}{2}\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}10x+\dfrac{4\pi}{5}=\pi-\dfrac{x}{2}+k2\pi\\10x+\dfrac{4\pi}{5}=\dfrac{x}{2}-\pi+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow...\)
\(24\times\left(15+30+85-120\right)\div16\)
\(=24\times10\div16\)
\(=15\)
\(140-180\times\left(47-90+43+7\right)\)
\(=140-\left(180\times7\right)\)
\(=140-1260\)
\(=-1120\)
x x 90 =180
x = 180 : 90
x = 2 ai k mk mk k lai
x = 2
mk tk bạn rồi nhé