The value of 1-cos- 6 1-cos- 3 1-cos 2- 3 1-cos 7- 6 is

The correct option is C 3 16 ( 1+cosπ nbsp; 6 nbsp; nbsp;) ( 1+cosπ nbsp; 3 nbsp; nbsp;) ( 1+cos 2π nbsp; 3 nbsp; nbsp;) ( 1+co ...

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Arithmetic Progression

The value of ...

Question

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{3}{16}

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\frac{3}{8}

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\frac{3}{4}

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\frac{1}{2}

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\frac{(1 + tan \frac{π}{6}) (1 - cot \frac{π}{6})}{(1 + cos \frac{π}{3}) (1 - sec \frac{π}{3})}

c o s \frac{2 π}{3} - c o s π + c o s \frac{4 π}{3} - c o s \frac{5 π}{3} + c o s 2 π - c o s \frac{7 π}{3} + . . . . + c o s \frac{40 π}{3} - c o s \frac{41 π}{3} = k

cos \frac{2 π}{3} - cos (π) + cos \frac{4 π}{3} - cos \frac{5 π}{3} + cos (2 π) - cos \frac{7 π}{3} + \dots + cos \frac{40 π}{3} - cos \frac{41 π}{3} = k

| 6 k |

θ

c o s θ = \frac{8}{17},

c o s (\frac{π}{6} + θ) + c o s (\frac{π}{4} - θ) + c o s (\frac{2 π}{3} - θ)

= (\frac{\sqrt{3} - 1}{2} + \frac{1}{\sqrt{2}}) \frac{23}{17}

(1 + cos \frac{π}{8}) (1 + cos \frac{3 π}{8}) (1 + cos \frac{5 π}{8}) (1 + cos \frac{7 π}{8})

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