Question

lf $0<x,y<\frac{\pi }{2}$ then the system of equations
$\sin x.\sin y=\frac{3}{4}$ and $\tan x.\tan y=3$ has a solution at

• A. $x=\frac{\pi }{6},y=\frac{\pi }{6}$
• B. $x=\frac{\pi }{3},y=\frac{\pi }{3}$
• C. $x=\frac{\pi }{12},y=\frac{\pi }{12}$
• D. $x=\frac{\pi }{4},y=\frac{\pi }{4}$

Answer 1

Answer: (B)

$x=\frac{\pi }{3},y=\frac{\pi }{3}$

at $x=\frac{\pi }{3},y=\frac{\pi }{3}$

$\sin x.\sin y=\frac{\sqrt{3}}{2}\ast \frac{\sqrt{3}}{2}=\frac{3}{4}\tan x.\tan y=\sqrt{3}\ast \sqrt{3}=3$

Therefore, Answer is $x=\frac{\pi }{3},y=\frac{\pi }{3}$