Find the value of - cos -33- cos2-65-4-65- cos8-65- cos16-65- cos32-65

Let #160; θ = π65 , n = 6 L.H.S = sin 2^6 θ 2^6 sin θ = 164sin 64 ·π65sin π65 = 164sin ( π π65 )sin π65 = 164 as sin ...

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Standard XII

Mathematics

Higher Order Derivatives

Find the valu...

Question

Find the value of :
$c o s \frac{π}{33} \cdot c o s \frac{2 π}{65} \cdot \frac{4 π}{65} \cdot c o s \frac{8 π}{65} \cdot c o s \frac{16 π}{65} \cdot c o s \frac{32 π}{65}$

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Solution

Let $θ = \frac{π}{65}, n = 6$
$L . H . S = \frac{s i n 2^{6} θ}{2^{6} s i n θ} = \frac{1}{64} \frac{s i n 64 \cdot \frac{π}{65}}{s i n \frac{π}{65}}$
$= \frac{1}{64} \frac{s i n (π - \frac{π}{65})}{s i n \frac{π}{65}} = \frac{1}{64}$ as sin ( $π - θ$ ) = sin $θ$

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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

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}

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Find the value of : cosπ33⋅cos2π65⋅4π65⋅cos8π65⋅cos16π65⋅cos32π65

Let θ=π65,n=6L.H.S=sin26θ26sinθ=164sin64⋅π65sinπ65=164sin(π−π65)sinπ65=164 as sin (π−θ) = sin θ

Find the value of :
$c o s \frac{π}{33} \cdot c o s \frac{2 π}{65} \cdot \frac{4 π}{65} \cdot c o s \frac{8 π}{65} \cdot c o s \frac{16 π}{65} \cdot c o s \frac{32 π}{65}$

Let $θ = \frac{π}{65}, n = 6$
$L . H . S = \frac{s i n 2^{6} θ}{2^{6} s i n θ} = \frac{1}{64} \frac{s i n 64 \cdot \frac{π}{65}}{s i n \frac{π}{65}}$
$= \frac{1}{64} \frac{s i n (π - \frac{π}{65})}{s i n \frac{π}{65}} = \frac{1}{64}$ as sin ( $π - θ$ ) = sin $θ$