The value of $\frac{sin 8 x + 7 sin 6 x + 18 sin 4 x + 12 sin 2 x}{sin 7 x + 6 sin 5 x + 12 sin 3 x}$ is equal to

2 cos x

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cos x

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2 sin x

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sin x

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Solution

The correct option is A $2 cos x$
Numerator of given expression

$= (sin 8 x + sin 6 x) + 6 (sin 6 x + sin 4 x) + 12 (sin 4 x + sin 2 x)$

$= 2 sin 7 x cos x + 12 sin 5 x cos x + 24 sin 3 x cos x$

$= 2 cos x (sin 7 x + 6 sin 5 x + 12 sin 3 x)$

Hence, given expression $= \frac{2 cos x (sin 7 x + 6 sin 5 x + 12 sin 3 x)}{sin 7 x + 6 sin 5 x + 12 sin 3 x} = 2 cos x$

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Similar questions

0 < x < π

\frac{sin 8 x + 7 sin 6 x + 18 sin 4 x + 12 sin 2 x}{sin 7 x + 6 sin 5 x + 12 sin 3 x}

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cos x - sin x = \sqrt{2} sin x

\int \frac{d x}{s i n x + s i n 2 x} =

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