làm giúp mình 9-19

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Câu 9. `\sin(\pi-x)-\cos x=0`

`⇔\sin x-\cos x=0⇔\cos x=\sin x`

`⇔\cosx=\cos(\pi/2-x)`

$⇔\left[ \begin{array}{l}x=\frac{\pi}{2}-x+k2\pi\\x=x-\frac{\pi}{2}+k2\pi(loại)\end{array} \right.⇔2x=\frac{\pi}{2}+k2\pi⇔x=\frac{\pi}{4}+k\pi$

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Câu 10. `\tan 3x=\cot x`$($ĐKXĐ: `x\in R\\{\pi/6+k{2\pi}/3;k\pi|k\in Z}`$)$

`⇔\tan 3x=\tan(\pi/2-x)⇔3x=\pi/2-x+k\pi`

`⇔x=\pi/8+k\pi/4` $($TMĐK$)$

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Câu 11. `\sin x.\sin(x-\pi/18)=0`

$⇔\left[ \begin{array}{l}\sin x=0\\\sin(x-\frac{\pi}{18})=0\end{array} \right.⇔\left[ \begin{array}{l}x=k\pi\\x-\frac{\pi}{18}=k\pi\end{array} \right.⇔\left[ \begin{array}{l}x=k\pi\\x=\frac{\pi}{18}+k\pi\end{array} \right.$

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Câu 12. `\sqrt3\sin3x-\cos3x=2`

`⇔\sqrt3/2.sin3x-1/2.\cos3x=1⇔\cos``\pi/6.\sin3x-\sin``\pi/6.\cos3x=1`

`⇔\sin(3x-\pi/6)=1=\sin``\pi/2`

`3x-\pi/6=\pi/2+k2\pi⇔x={2\pi}/9+k{2\pi}/3`

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Câu 13. `\tan x+2\cot x=3` $($ĐKXĐ`:x\in R\\{k\pi/2|k\in Z}`$)$

`⇔\tan x+2/{\tan x}=3⇔{\tan^2x+2}/{\tan x}=3`

`⇒\tan^2x-3\tan x+2=0⇔(\tan x-1)(\tan x-2)=0`

$⇔\left[ \begin{array}{l}\tan x=1=\tan\frac{\pi}{4}\\\tan x=2=\tan(\tan^{-1}2)\end{array} \right.⇔\left[ \begin{array}{l}x=\frac{\pi}{4}+k\pi\\x=\tan^{-1}2+k\pi\end{array} \right.$

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Câu 14. `2\sin^2x-3\sin x+1=0`

$⇔(2\sin x-1)(\sin x-1)=0⇔\left[ \begin{array}{l}\sin x=\frac{1}{2}=\sin\frac{\pi}{6}\\\sin x=1=\sin\frac{\pi}{2}\end{array} \right.$

$⇔\left[ \begin{array}{l}x=\frac{\pi}{6}+k2\pi\\x=\pi-\frac{\pi}{6}+k2\pi=\frac{5\pi}{6}+k2\pi\\x=\frac{\pi}{2}+k2\pi\end{array} \right.$

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Câu 15. `\sin2x-\cos x-2\sin x+1=0`

`⇔2\sin x\cos x-\cos x-2\sin x+1=0`

`⇔2\sin x(\cos x-1)-(\cos x-1)=0`

`⇔(2\sin x-1)(\cos x-1)=0`

$⇔\left[ \begin{array}{l}\sin x=\frac{1}{2}=\sin\frac{\pi}{6}\\\cos x=1=\cos0\end{array} \right.⇔\left[ \begin{array}{l}x=\frac{\pi}{6}+k2\pi\\x=\pi-\frac{\pi}{6}+k2\pi=\frac{5\pi}{6}+k2\pi\\x=k2\pi\end{array} \right.$

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Câu 16. `\sqrt3\sin x-\cos x=0`

`⇔\sqrt3/2\sin x-1/2\cos x=0`

`⇔\sin\frac{\pi}{3}.\sin x-\cos\frac{\pi}{3}.\cos x=0`

`⇔\cos(x+\pi/3)=0=\cos\frac{\pi}{2}⇔x+\pi/3=\pi/2+k\pi`

`⇔x=\pi/6+k\pi`

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Câu 17. `\cos2x-3\cos x+2=0`

`⇔2\cos^2x-1-3\cos x+2=0`

`⇔2\cos^2x-3\cos x+1=0`

$⇔(2\cos x-1)(\cos x-1)=0⇔\left[ \begin{array}{l}\cos x=\frac{1}{2}=\cos\frac{\pi}{3}\\\cos x=1=\cos0\end{array} \right.$

$⇔\left[ \begin{array}{l}x=±\frac{\pi}{3}+k2\pi\\x=k2\pi\end{array} \right.$

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Câu 18. `\sin7x.\sin x=\sin5x.\sin3x`

`⇔1/2[\cos(7x-x)-\cos(7x+x)]=1/2[\cos(5x-3x)-\cos(5x+3x)]`

`⇔\cos6x-\cos8x=\cos2x-\cos8x⇔\cos6x=\cos2x`

$⇔\left[ \begin{array}{l}6x=2x+k2\pi\\6x=-2x+k2\pi\end{array} \right.⇔\left[ \begin{array}{l}x=k\frac{\pi}{2}\\x=k\frac{\pi}{4}\end{array} \right.⇔x=k\frac{\pi}{4}$