Cos-7-cos3 -7-cos5 -7 are the roots of the equation 8 x3-4 x2-4 x-1-0 - Then the value of -7-3 -7-5 -7 iA- None of theseB- 2C- 4D- 8

The correct option is C 4 secπ/7+sec3π/7+sec5π/7 =1/cosπ/7+1/cos3π/7+1/cos5π/7 =cos3π/7.cos5π/7+cosπ/7.cos5π/7+cosπ/7.cos3π/7/cosπ/7.cos3π/7.cos5π/7 =∑αβ/∑α ...

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Byju's Answer

Standard XII

Mathematics

General Solutions of (sin theta)^2 = (sin alpha)^2 , (cos theta)^2 = (cos alpha)^2 , (tan theta)^2 = (tan alpha)^2

cosπ/7·cos3 π...

Question

$c o s \frac{π}{7}$ . $c o s \frac{3 π}{7}$ . $c o s \frac{5 π}{7}$ are the roots of the equation $8 x^{3} - 4 x^{2} - 4 x + 1 = 0$ . Then the value of $s e c \frac{π}{7} + s e c \frac{3 π}{7} + s e c \frac{5 π}{7}$ is

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None of these

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Solution

The correct option is B
4

$s e c \frac{π}{7} + s e c \frac{3 π}{7} + s e c \frac{5 π}{7} = \frac{1}{c o s \frac{π}{7}} + \frac{1}{c o s \frac{3 π}{7}} + \frac{1}{c o s \frac{5 π}{7}} = \frac{c o s \frac{3 π}{7} . c o s \frac{5 π}{7} + c o s \frac{π}{7} . c o s \frac{5 π}{7} + c o s \frac{π}{7} . c o s \frac{3 π}{7}}{c o s \frac{π}{7} . c o s \frac{3 π}{7} . c o s \frac{5 π}{7}} = \frac{\sum α β}{\sum α β γ} = \frac{\frac{- 4}{8}}{\frac{- 1}{8}} = 4$

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Similar questions

Q. If

cos \frac{π}{7}, cos \frac{3 π}{7}, cos \frac{5 π}{7}

are the roots of the equation

8 x^{3} - 4 x^{2} - 4 x + 1 = 0

The value of

sec \frac{π}{7} + sec \frac{3 π}{7} + sec \frac{5 π}{7} =

Q. If the roots of the equation

8 x^{3} - 4 x^{2} - 4 x + 1 = 0

are

cos \frac{π}{7}, cos \frac{3 π}{7}, cos \frac{5 π}{7}

, then show that

sec \frac{π}{7} + sec \frac{3 π}{7} + sec \frac{5 π}{7} = 4

$c o s \frac{π}{7}$ . $c o s \frac{3 π}{7}$ . $c o s \frac{5 π}{7}$ are the roots of the equation $8 x^{3} - 4 x^{2} - 4 x + 1 = 0$ . Then the value of $s i n \frac{π}{14} . s i n \frac{3 π}{14} . s i n \frac{5 π}{14}$ is

Q. If

cos \frac{2 π}{7}, cos \frac{4 π}{7}, cos \frac{6 π}{7}

are roots of the equation

8 x^{3} + 4 x^{2} - 4 x - 1 = 0

.The value of

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

is equal to

Q. The value of

cos 0 + cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7} =

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cosπ7. cos3π7. cos5π7 are the roots of the equation 8x3−4x2−4x+1=0. Then the value of secπ7+sec3π7+sec5π7 is

The correct option is B 4 secπ7+sec3π7+sec5π7=1cosπ7+1cos3π7+1cos5π7=cos3π7.cos5π7+cosπ7.cos5π7+cosπ7.cos3π7cosπ7.cos3π7.cos5π7=∑αβ∑αβγ=−48−18=4

$c o s \frac{π}{7}$ . $c o s \frac{3 π}{7}$ . $c o s \frac{5 π}{7}$ are the roots of the equation $8 x^{3} - 4 x^{2} - 4 x + 1 = 0$ . Then the value of $s e c \frac{π}{7} + s e c \frac{3 π}{7} + s e c \frac{5 π}{7}$ is