Question

If $\sin (x-y)=\cos (x+y)=1 / 2$, then the values of $x$ and $y$ lying between $0^{\circ}$ and $180^{\circ}$ are

• A. $x=45^{\circ}, y=15^{\circ}$
• B. $x=45^{\circ}, y=135^{\circ}$
• C. $x=165^{\circ}, y=15^{\circ}$
• D. $x=165^{\circ}, y=135^{\circ}$

Answer 1

Answer: (A)

$\sin (x-y)=1 / 2 $
$\Rightarrow x-y=\pi / 6$ or $\frac{5 \pi}{6}$
$\cos (x+y)=1 / 2 $
$\Rightarrow x+y=\frac{\pi}{3}, \frac{5 \pi}{6}$
$\therefore $ After solving we get $x=45^{\circ}, y=15^{\circ}$