Write the value of cos-7cos2 -7cos4 -7

Cos π/7 cos 2 π/7 cos 4 π/7 =2 sin π/7. cos π/7. cos 2 π/7. cos 4 π/7/2 sin π/7 [Divide and multiply by 2 sin π/7] = 2.sin 2 π/7. cos 2 π/7. cos 4 π/7/2.2 sin ...

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Standard XII

Mathematics

Trigonometric Ratios of Multiples of an Angle

Write the val...

Question

Write the value of $c o s \frac{π}{7} c o s \frac{2 π}{7} c o s \frac{4 π}{7}$ .

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Solution

$c o s \frac{π}{7} c o s \frac{2 π}{7} c o s \frac{4 π}{7} = \frac{2 s i n \frac{π}{7} . c o s \frac{π}{7} . c o s \frac{2 π}{7} . c o s \frac{4 π}{7}}{2 s i n \frac{π}{7}}$

[Divide and multiply by $2 s i n \frac{π}{7}$ ]

$= \frac{2. s i n \frac{2 π}{7} . c o s \frac{2 π}{7} . c o s \frac{4 π}{7}}{2.2 s i n \frac{π}{7}} = \frac{2 s i n \frac{4 π}{7} . c o s \frac{4 π}{7}}{2.4 s i n \frac{π}{7}} = \frac{s i n \frac{8 π}{7}}{8 s i n \frac{π}{7}} = \frac{s i n (π + \frac{π}{7})}{8 s i n \frac{π}{7}} = \frac{- s i n \frac{π}{7}}{8 s i n \frac{π}{7}} = \frac{- 1}{8}$

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Similar questions

cos \frac{π}{7} cos \frac{2 π}{7} cos \frac{4 π}{7} = ?

cos \frac{π}{7} cos \frac{2 π}{7} cos \frac{4 π}{7} =

Q. Prove that:

cos \frac{π}{7} cos \frac{2 π}{7} cos \frac{4 π}{7} = - \frac{1}{8}

Q. The value of

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

Q. Assertion :

cos \frac{π}{7} cos \frac{2 π}{7} cos \frac{4 π}{7} = \frac{1}{8}

Reason:

cos θ cos 2 θ cos 4 θ . . . cos 2^{n - 1} θ = \frac{1}{2^{n}}

, if

θ = \frac{π}{2^{n} - 1}

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Write the value of cos π7 cos 2π7 cos 4π7.

cos π7 cos 2π7 cos 4π7=2 sin π7. cos π7. cos 2π7. cos 4π72 sin π7 [Divide and multiply by 2 sin π7] =2.sin 2π7. cos 2π7. cos 4π72.2sin π7=2 sin 4π7. cos 4π72.4 sin π7=sin 8π78 sin π7=sin(π+π7)8 sin π7=−sinπ78 sin π7=−18

Write the value of $c o s \frac{π}{7} c o s \frac{2 π}{7} c o s \frac{4 π}{7}$ .