Question

The smallest positive values of x and y which satisfy $tan(x–y)=1,sec(x+y)=\frac{2}{\sqrt{3}}$ are

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$tan(x-y)=1\Rightarrow x-y=\frac{\pi }{4}sec(x+y)=\frac{2}{\sqrt{3}}\Rightarrow x+y=2\pi -\frac{\pi }{6}=\frac{11\pi }{6}\Rightarrow x=\frac{25\pi }{24},y=\frac{19\pi }{24}$