Find the value of the following.

$\frac{sin67°cos37°-sin37°cos67°}{cos13°cos17°-sin13°sin17°}$

$\frac{1}{\sqrt{3}}$

sinA = cosB  Iff A + B = 90º

$\frac{sin67°cos37°-sin37°cos67°}{cos13°cos17°-sin13°sin17°}$

= $\frac{cos23°cos37°-sin37°sin23°}{cos13°cos17°-sin13°sin17°}$

{ using , cos(A+B) = cosA.cosB - sinA.sinB }

= $\frac{cos ( 23° + 37°)}{ cos ( 13° + 17°) }$

= $\frac{cos 60°}{ cos30° }$

= $\frac{1/2}{ √3/2 }$

= $\frac{1}{ √3 }$