The value of cos-65cos2 -65cos4 -65cos8 -65cos16 -65cos32 -65 is

The correct option is B none of these We have, cos π/65 cos 2 π/65 cos 4 π/65 cos 8 π/65 cos 16 π/65 cos 32 π/65 = 2 sin π/65/2 sin π/65 cos π/65 cos 2 π/65 co ...

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Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

The value of ...

Question

The value of $c o s \frac{π}{65} c o s \frac{2 π}{65} c o s \frac{4 π}{65} c o s \frac{8 π}{65} c o s \frac{16 π}{65} c o s \frac{32 π}{65}$ is

$\frac{1}{8}$

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$\frac{1}{16}$

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$\frac{1}{32}$

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none of these

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Solution

The correct option is D
none of these

We have,

$c o s \frac{π}{65} c o s \frac{2 π}{65} c o s \frac{4 π}{65} c o s \frac{8 π}{65} c o s \frac{16 π}{65} c o s \frac{32 π}{65}$

$= \frac{2 s i n \frac{π}{65}}{2 s i n \frac{π}{65}} c o s \frac{π}{65} c o s \frac{2 π}{65} c o s \frac{4 π}{65} c o s \frac{8 π}{65} c o s \frac{16 π}{65} c o s \frac{32 π}{65}$

(dividing and multiplying by 2 sin $\frac{π}{65}$ )

$= \frac{2 s i n \frac{2 π}{65}}{2 \times 2 s i n \frac{π}{65}} c o s \frac{2 π}{65} c o s \frac{4 π}{65} c o s \frac{8 π}{65} c o s \frac{16 π}{65} c o s \frac{32 π}{65} = \frac{2 s i n \frac{4 π}{65}}{2 \times 4 s i n \frac{π}{65}} c o s \frac{4 π}{65} c o s \frac{8 π}{65} c o s \frac{16 π}{65} c o s \frac{32 π}{65} = \frac{2 s i n \frac{8 π}{65}}{2 \times 8 s i n \frac{π}{65}} c o s \frac{8 π}{65} c o s \frac{16 π}{65} c o s \frac{32 π}{65} = \frac{2 s i n \frac{16 π}{65}}{2 \times 16 s i n \frac{π}{65}} c o s \frac{16 π}{65} c o s \frac{32 π}{65} = \frac{2 s i n \frac{32 π}{65}}{2 \times 32 s i n \frac{π}{65}} c o s \frac{32 π}{65}$

$= \frac{s i n \frac{64 π}{65}}{64 s i n \frac{π}{65}} = \frac{s i n (π - \frac{π}{65})}{64 s i n \frac{π}{65}} = \frac{s i n \frac{π}{65}}{64 s i n \frac{π}{65}} = \frac{1}{64}$

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Similar questions

Q. Find :

cos \frac{π}{65} cos \frac{2 π}{65} cos \frac{4 π}{65} cos \frac{8 π}{65} cos \frac{16 π}{65} cos \frac{32 π}{65}

$c o s \frac{π}{65} c o s \frac{2 π}{65} c o s \frac{4 π}{65} c o s \frac{8 π}{65} c o s \frac{16 π}{65} c o s \frac{32 π}{65} = \frac{1}{64}$

Q. Find the value of :

c o s \frac{π}{33} \cdot c o s \frac{2 π}{65} \cdot \frac{4 π}{65} \cdot c o s \frac{8 π}{65} \cdot c o s \frac{16 π}{65} \cdot c o s \frac{32 π}{65}

Q. The value of

cos \frac{π}{7} cos \frac{2 π}{7} cos \frac{3 π}{7}

Q. The value of

cos \frac{π}{2^{2}} \cdot cos \frac{π}{2^{3}} \cdot . . . \cdot cos \frac{π}{2^{10}} \cdot sin \frac{π}{2^{10}}

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The value of cos π65 cos 2π65 cos 4π65 cos 8π65 cos 16π65 cos 32π65 is

The value of $c o s \frac{π}{65} c o s \frac{2 π}{65} c o s \frac{4 π}{65} c o s \frac{8 π}{65} c o s \frac{16 π}{65} c o s \frac{32 π}{65}$ is