A solution (x,y) of the system of equations x−y=13 and cos2(πx)−sin2(πy)=12 is given by

cos(πx+πy)cos(πx−πy)=12 cos(π(x+y))=1x+y=2, x−y=13x=6+16,y=6−16

A solution (x,y) of the system of equations x−y=13 and cos2(πx)−sin2(πy)=12 is given by

cos(πx+πy)cos(πx−πy)=12 cos(π(x+y))=1x+y=2, x−y=13x=6+16,y=6−16

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A solution (x,y) of the system of equations $x - y = \frac{1}{3} a n d \cos^{2} (π x) - \sin^{2} (π y) = \frac{1}{2}$ is given by

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${\frac{7}{6}, \frac{5}{6}}$

${\frac{- 2}{3}, - \frac{1}{3}}$

${\frac{1}{6}, \frac{5}{6}}$

${\frac{2}{3}, \frac{1}{3}}$

answer is A.

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Detailed Solution

$\cos (π x + π y) \cos (π x - π y) = \frac{1}{2}$

$\cos (π (x + y)) = 1$

$x + y = 2, x - y = \frac{1}{3}$

$x = \frac{6 + 1}{6}, y = \frac{6 - 1}{6}$

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A solution (x,y) of the system of equations x−y=13 and cos2(πx)−sin2(πy)=12 is given by

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A solution (x,y) of the system of equations $x - y = \frac{1}{3} a n d \cos^{2} (π x) - \sin^{2} (π y) = \frac{1}{2}$ is given by