Find the general solutions of the following equations: 9x= - Vidyadip

Question

Find the general solutions of the following equations:
$\sin9\text{x}=\sin\text{x}$

✓

Answer

$\sin9\text{x}=\sin\text{x}$
$\sin9\text{x}-\sin\text{x}=0$
Apply $\sin\text{A}-\sin\text{B}$ Formula
$\sin\text{A}-\sin\text{B}=2\cos\Big(\frac{\text{A+B}}{2}\Big)\sin\Big(\frac{\text{A-B}}{2}\Big)$
$\sin9\text{x}-\sin\text{x}2\cos5\text{x}\sin4\text{x}=0$
$\cos5\text{x}\sin4\text{x}=0$
$\Rightarrow\cos5\text{x}=0$ or $\sin4\text{x}=0$
$5\text{x}=\frac{(2\text{n}+1)\pi}{2}$ (or) $4\text{x}=\text{n}\pi$
$\text{x}=\Big\{\frac{(2\text{n}+1)\pi}{10}\Big\}$ {or}$\text{x}=\Big\{\frac{\text{n}\pi}{4}\Big\}$where$\text{n}\in\text{z}$

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