$\frac{s i n 7 x + 6 s i n 5 x + 17 s i n 3 x + 12 s i n x}{s i n 6 x + 5 s i n 4 x + 12 s i n 2 x}$
is equal to

c o s x

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2 c o s x

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s i n x

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2 s i n x

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Solution

The correct option is B $2 c o s x$
$\frac{s i n 7 x + 6 s i n 5 x + 17 s i n 3 x + 12 s i n x}{s i n 6 x + 5 s i n 4 x + 12 s i n 2 x} = \frac{(s i n 7 x + s i n 5 x) + 5 (s i n 5 x + s i n 3 x) + 12 (s i n 3 x + s i n x)}{s i n 6 x + 5 s i n 4 x + 12 s i n 2 x} = \frac{2 s i n 6 x c o s x + 10 s i n 4 x c o s x + 12 s i n 2 x c o s x}{s i n 6 x + 5 s i n 4 x + 12 s i n 2 x} = \frac{2 c o s x (s i n 6 x + 5 s i n 4 x + 12 s i n 2 x)}{s i n 6 x + 5 s i n 4 x + 12 s i n 2 x} = 2 c o s x$

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