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 $x=45^{\circ },y=15^{\circ }$