Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

Adding and subtracting the equations yields $\cos (x-y)=\sqrt{3}/2$ and $\cos (x+y)=0$. Thus $x-y=2n\pi \pm \pi /6$, $x+y=k\pi +\pi /2$. The plus and minus branches give the two pairs $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ listed in A-D; each formula is part of a valid paired branch.