If x = sin 7 2 π + sin 7 4 π + sin 7 8 π and y = cos 7 2 π + cos 7 4 π + cos 7 8 π , then x 2 + y 2 =

x 2 + y 2 = 3 + 2 ( cos 7 2 π + cos 7 4 π + cos 7 6 π ) = 3 + 2 ( − 2 1 ) = 2

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MathematicsTrigonometric Ratios & IdentitiesSummation of SeriesMedium2 minQB

MathematicsMediumsingle choice

If $x = sin \frac{2 π}{7} + sin \frac{4 π}{7} + sin \frac{8 π}{7}$ and $y = cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{8 π}{7}$ , then $x^{2} + y^{2} =$

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Solution:

$x^{2} + y^{2} = 3 + 2 (cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{6 π}{7}) = 3 + 2 (- \frac{1}{2}) = 2$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Summation of Series

⏱ 2mℹ️ Source: QB

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