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Cos8xcosx-sin8xsinx  write as a single trigonometric function ?

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\textit{Sum and Difference Identities} \\\\ \cos(\alpha + \beta)= \cos(\alpha)\cos(\beta)- \sin(\alpha)\sin(\beta) \\\\[-0.35em] ~\dotfill\\\\ \cos(8x)\cos(x)-\sin(8x)\sin(x)\implies \cos(8x+x)\implies \cos(9x)

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