The value of 1+cos⁡π61+cos⁡π3 1+cos⁡2π31+cos⁡7π6 is m16 Value of m is

=1+cos⁡π61+cos⁡π31+cos⁡2π31+cos⁡7π6=1+321+121−121−32=1−341−14=14×34=316

The value of 1+cos⁡π61+cos⁡π3 1+cos⁡2π31+cos⁡7π6 is m16 Value of m is

=1+cos⁡π61+cos⁡π31+cos⁡2π31+cos⁡7π6=1+321+121−121−32=1−341−14=14×34=316

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The value of $(1 + \cos \frac{π}{6}) (1 + \cos \frac{π}{3}) (1 + \cos \frac{2 π}{3}) (1 + \cos \frac{7 π}{6}) is \frac{m}{16}$ Value of m is

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$\frac{3}{16}$

answer is D.

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Detailed Solution

$\begin{array}{l} = (1 + \cos \frac{π}{6}) (1 + \cos \frac{π}{3}) (1 + \cos \frac{2 π}{3}) (1 + \cos \frac{7 π}{6}) \\ = (1 + \frac{\sqrt{3}}{2}) (1 + \frac{1}{2}) (1 - \frac{1}{2}) (1 - \frac{\sqrt{3}}{2}) \\ = (1 - \frac{3}{4}) (1 - \frac{1}{4}) = \frac{1}{4} \times \frac{3}{4} = \frac{3}{16} \end{array}$