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Prove that ...

Question

Prove that $\frac{cos 7 x + cos 5 x}{sin 7 x - sin 5 x} = cot x$

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Solution

Applying the trigonometric identities in the LHS of the $\frac{cos 7 x + cos 5 x}{sin 7 x - sin 5 x} = cot x$ .

$\frac{cos 7 x + cos 5 x}{sin 7 x - sin 5 x} = \frac{2 cos 6 x cos x}{2 cos 6 x sin x}$

$= \frac{cos x}{sin x}$

$= cot x$

$= R H S$

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