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sir please tell what is the integration of sin9x / sinx?

sir please tell what is the integration of sin9x / sinx?

Grade:12

1 Answers

jagdish singh singh
173 Points
7 years ago
\hspace{-0.6 cm}\int\frac{\sin 9x}{\sin x}dx = \int\frac{\sin 9x-\sin 7x+\sin 7x-\sin 5x+\sin 5x-\sin 3x+\sin 3x-\sin x+\sin x}{\sin x}$\\\\\\Using $\sin C-\sin D=2\cos \frac{C+D}{2}\sin \frac{C-D}{2}$\\\\\\So $\int\frac{\sin 9x}{\sin x}dx = \int \left(\cos 8x+\cos 6x+\cos 4x+\cos 2x+1\right)dx$\\\\\\So $\int\frac{\sin 9x}{\sin x}dx = \frac{\sin 8x}{8}+\frac{\sin 6x}{6}+\frac{\sin 4x}{4}+\frac{\sin 2x}{2}+x+\mathcal{C}$

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