$cos 12 cos 24 cos 36 cos 48 cos 72 cos 96$ equals

- \frac{1}{2^{6}}

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\frac{1}{2^{8}}

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\frac{1}{2^{7}}

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- \frac{1}{2^{7}}

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Solution

The correct option is B $- \frac{1}{2^{6}}$
Given, $c o s 12. c o s 24. c o s 36. c o s 48. c o s 72. c o s 96$

$= \frac{2 s i n 12. c o s 12. c o s 24. c o s 48. c o s 96. c o s 36. c o s 72}{2 s i n 12}$

$= \frac{2 s i n 24. c o s 24. c o s 48. c o s 96. c o s 36. c o s 72}{4 s i n 12}$

$= \frac{2 s i n 48 c o s 48. c o s 96. c o s 36. c o s 72}{8 s i n 12}$

$= \frac{2 s i n 96. c o s 96. c o s 36. c o s 72}{16 s i n 12}$

$= \frac{s i n 192. c o s 36. c o s 72}{16 s i n 12} = \frac{s i n (180 + 12) . c o s 36. c o s 72}{16 s i n 12}$

$= - \frac{1}{16} c o s 36. c o s 72 = - \frac{1}{16} (\frac{\sqrt{5} - 1}{4}) (\frac{\sqrt{5} + 1}{4})$

$= - \frac{1}{64} = - \frac{1}{2^{6}}$

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cos12cos24cos36cos48cos72cos96 equals

$cos 12 cos 24 cos 36 cos 48 cos 72 cos 96$ equals