Find the value of the following.
$\frac{sin67°cos37°-sin37°cos67°}{cos13°cos17°-sin13°sin17°}$
Answer & explanation
Correct answer: option 1
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 }
= $\frac{cos ( 23° + 37°)}{ cos ( 13° + 17°) }$
= $\frac{cos 60°}{ cos30° }$
= $\frac{1/2}{ √3/2 }$
= $\frac{1}{ √3 }$