Find the value of x- -7 - 3-7 - 5-7 - -

#160; π #160; 7 #160; 2π #160; 7 #160; 3π #160; 7 #160; = 1 cos #160; π #160; 7 cos #160; 2π #160; 7 cos #160; 3π ...

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Byju's Answer

Standard XII

Mathematics

Summation by Sigma Method

Find the valu...

Question

Find the value of x:
$sec \frac{π}{7} + sec \frac{3 π}{7} + sec \frac{5 π}{7} = ?$

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Solution

$sec \frac{π}{7} sec \frac{2 π}{7} sec \frac{3 π}{7} = \frac{1}{cos \frac{π}{7} cos \frac{2 π}{7} cos \frac{3 π}{7}} = \frac{sin \frac{π}{7}}{sin \frac{π}{7} cos \frac{π}{7} + cos \frac{2 π}{7} cos \frac{3 π}{7}} = \frac{2 sin \frac{π}{7}}{2 sin \frac{π}{7} cos \frac{π}{7} + cos \frac{2 π}{7} cos \frac{3 π}{7}} = \frac{2 \times 2 sin \frac{π}{7}}{2 \times sin \frac{2 π}{7} cos \frac{2 π}{7} \frac{3 π}{7}} = \frac{4 sin \frac{π}{7}}{sin \frac{4 π}{7} . cos \frac{3 π}{7}} a n d cos \frac{3 π}{7} = - cos (π - \frac{3 π}{7}) = - cos \frac{4 π}{7} T h e n, \frac{4 sin \frac{π}{7}}{sin \frac{4 π}{7} . cos \frac{3 π}{7}} = \frac{2 \times 4 sin \frac{π}{7}}{2 \times sin \frac{4 π}{7} cos \frac{3 π}{7}} = \frac{8 \times sin \frac{π}{7}}{- sin (\frac{8 π}{7})} a g a i n sin (\frac{8 π}{7}) = sin (π + \frac{π}{7}) = - sin (\frac{π}{7}) N o w, \frac{8 \times sin \frac{π}{7}}{- sin (\frac{8 π}{7})} = \frac{8 \times sin \frac{π}{7}}{- (- sin (\frac{8 π}{7}))} = 8$

Hence,the value of $x$ is $8$ .

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Similar questions

Q. If

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Find the value of x:secπ7+sec3π7+sec5π7=?

Find the value of x:
$sec \frac{π}{7} + sec \frac{3 π}{7} + sec \frac{5 π}{7} = ?$