मराठी

Find the General Solution of the Following Equation: Sin 9 X = Sin X

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प्रश्न

Find the general solution of the following equation:

\[\sin 9x = \sin x\]
बेरीज
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उत्तर

We have:

\[\sin9x = \sin x\]

⇒ \[\sin9x - \sin x = 0\]

⇒ \[2 \sin \left( \frac{9x - x}{2} \right) \cos \left( \frac{9x + x}{2} \right) = 0\]

⇒ \[\sin \frac{8x}{2} = 0\] 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 \[x = (2n + 1)\frac{\pi}{10}\],

\[n \in Z\]
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पाठ 11: Trigonometric equations - Exercise 11.1 [पृष्ठ २१]

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आर.डी. शर्मा Mathematics [English] Class 11
पाठ 11 Trigonometric equations
Exercise 11.1 | Q 2.03 | पृष्ठ २१

व्हिडिओ ट्यूटोरियलVIEW ALL [1]

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