Question

A solution (x,y) of the system of equation x-y=1/3 and cos^2(pix)- sin^2(piy)=1/2 is given by

Answer 1

Step-by-step explanation:

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Answer 2

Answer: $x=\frac{1}{6}$ and y=$-\frac{1}{6}$.

Step-by-step explanation:

• Given, x - y=$\frac{1}{3}$ and $cos^{2}(\pi x) - sin^{2} (\pi x)=\frac{1}{2}$
• We know that, $cos^{2}(\pi x) - sin^{2} (\pi x)=cos(2\pi x)$
• So, $cos(2\pi x)=\frac{1}{2}$

          ⇒ $2\pi x=cos^{-1}( \frac{1}{2})$

          ⇒ $2\pi x=\frac{\pi }{3}$

          ⇒ $x=\frac{1}{6}$

• Putting in the above equation we get, y=$-\frac{1}{6}$.
• Hence the value of x and y are $\frac{1}{6} \ and \ (-\frac{1}{6})$ respectively.

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