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Question
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8 cos x
cos x
8 sin x
sin x
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Solution
sin x
\[\text{ We have } , 8\sin\frac{x}{8} \cos\frac{x}{2} \cos\frac{x}{4} \cos\frac{x}{8}\]
\[ = 4 \times \left( 2\sin\frac{x}{8} \cos\frac{x}{8} \right) \cos\frac{x}{2} \cos\frac{x}{4}\]
\[ = 4 \times \sin\frac{x}{4}\cos\frac{x}{2} \cos\frac{x}{4}\]
\[ = 2 \times \left( 2\sin\frac{x}{4} \cos\frac{x}{4} \right) \cos\frac{x}{2}\]
\[ = 2 \times \sin\frac{x}{2}\cos\frac{x}{2}\]
\[ = \text{ sin } x\]
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