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Parametric Differentiation

Evaluate co...

Question

Evaluate $\frac{cos 9 x - cos 5 x}{sin 17 x - sin 3 x} = \frac{- sin 2 x}{cos 10 x}$

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Solution

Applying transformation,
$\frac{- 2 sin (\frac{9 x + 5 x}{2}) sin (\frac{9 x - 5 x}{2})}{2 cos (\frac{17 x + 3 x}{2}) sin (\frac{17 x - 3 x}{2})} = \frac{- 2 sin 7 x sin 2 x}{2 cos 10 x sin 7 x} = - \frac{sin 2 x}{cos 10 x}$

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\frac{cos 9 x - cos 5 x}{sin 17 x - sin 3 x} = - \frac{sin 2 x}{cos 10 x}

\frac{cos 9 x - cos 5 x}{sin 17 x - sin 3 x} = - \frac{sin 2 x}{cos 10 x}

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lim x \to 0 \frac{sin 7 x - sin 5 x + sin 3 x - sin x}{sin 6 x - sin 4 x + sin 2 x}

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