$\frac{sin 5 x + sin 3 x}{cos 5 x + cos 3 x} =$

tan 3 x

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tan 2 x

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tan 4 x

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tan x

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Solution

The correct option is B $tan 4 x$
$\frac{sin 5 x + sin 3 x}{cos 5 x + cos 3 x}$

$= \frac{2 sin (\frac{5 x + 3 x}{2}) cos (\frac{5 x - 3 x}{2})}{2 cos (\frac{5 x + 3 x}{2}) cos (\frac{5 x - 3 x}{2})}$

$= \frac{2 sin 4 x cos x}{2 cos 4 x cos x}$

$= tan 4 x$

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