삼각함수 합 조건

$\sin x + \sin y = 1$에서 $\sin ^{2} x + \sin ^{2} y + 2 \sin x \sin y = 1$ …… ㉠ $\displaystyle \cos x + \cos y = \frac{1}{2}$에서 $\displaystyle \cos ^{2} x + \cos ^{2} y + 2 \cos x \cos y = \frac{1}{4}$ …… ㉡ ㉠＋㉡에서 $\displaystyle 2 + 2 ( \sin x \sin y + \cos x \cos y ) = \frac{5}{4}$ $\displaystyle 2 + 2 \cos ( x - y ) = \frac{5}{4}$ $\displaystyle \therefore \cos ( x - y ) = \frac{1}{2} \left( \frac{5}{4} - 2 \right) = - \frac{3}{8}$