Question

$0<x<2\pi ;0<y<2\pi$ and $3^{\sin x+cosy}=1$ and ${25}^{sin{x}^2+{\cos }^{2}y}=5$ then (x,y) is

• A. $(\frac{7\pi }{6},\frac{\pi }{3})$
• B. $(\frac{7\pi }{6},\frac{5\pi }{3})$
• C. $(\frac{11\pi }{6},\frac{\pi }{3})$
• D. $(\frac{11\pi }{6},\frac{5\pi }{3})$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $(\frac{7\pi }{6},\frac{5\pi }{3})$
B $(\frac{7\pi }{6},\frac{\pi }{3})$
C $(\frac{11\pi }{6},\frac{5\pi }{3})$
D $(\frac{11\pi }{6},\frac{\pi }{3})$

from first equation we get
$\sin x+\cos y=0$
and from second equation we get
${\sin }^{2}x+{\cos }^{2}y=\frac{1}{2}$
but from first equation , ${\sin }^{2}x={\cos }^{2}y$
put this in second we get
${\sin }^{2}x={\cos }^{2}y=\frac{1}{4}$
so all of $A,B,C,D$ are true