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Question
Find the general solution of the following equation:
Solution
We have:
⇒ \[\sin9x - \sin x = 0\]
⇒ \[2 \sin \left( \frac{9x - x}{2} \right) \cos \left( \frac{9x + x}{2} \right) = 0\]
⇒ \[\sin \frac{8x}{2} = 0\] or \[\cos \frac{10x}{2} = 0\]
⇒ \[\sin 4x = 0\] or \[\cos 5x = 0\]
⇒ \[4x = n\pi\]
\[n \in Z\] or \[5x = (2n + 1)\frac{\pi}{2}\],
\[n \in Z\]
⇒ \[x = \frac{n\pi}{4}\],
\[n \in Z\] or \[x = (2n + 1)\frac{\pi}{10}\],
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