MathDB

Let

S

be the set of all points

(x,y)

in the coordinate plane such that

0\le x\le \frac \pi2

and

0\le y\le \frac \pi2

. What is the area of the subset of

S

for which \sin^2 x \minus{} \sin x\sin y \plus{} \sin^2 y\le \frac 34?

<span class='latex-bold'>(A) </span> \frac {\pi^2}9 \qquad <span class='latex-bold'>(B) </span> \frac {\pi^2}8 \qquad <span class='latex-bold'>(C) </span> \frac {\pi^2}6\qquad <span class='latex-bold'>(D) </span> \frac {3\pi^2}{16} \qquad <span class='latex-bold'>(E) </span> \frac {2\pi^2}9

Problem Statement