Question

The solution (x, y) of the system of equations $x-y=\frac{1}{3}\text{and}{\cos }^2\left(\pi x\right)-{\sin }^2\left(\pi y\right)=\frac{1}{2}$ is given by

• A. $(\frac{13}{6},\frac{11}{6})$
• B. $(\frac{7}{6},\frac{5}{6})$
• C. $(\frac{1}{3},\frac{2}{3})$
• D. $(\frac{-5}{6},\frac{-7}{6})$

Answer 1

Answer: (A), (B), (D)

$(\frac{-5}{6},\frac{-7}{6})$

$(x-y)=\frac{1}{3}{\cos }^2\left(\pi x\right)-{\sin }^2\left(\pi y\right)=\frac{1}{2}$

$\Rightarrow x=\frac{7}{6},y=\frac{5}{6}$

$x=\frac{-5}{6},y=\frac{-7}{6}$

$x=\frac{13}{6},y=\frac{11}{6}$