Question

Evaluate:

${\displaystyle \frac{3{\sin 72}^{\circ }}{{\cos 18}^{\circ }}-\frac{{\sec 32}^{\circ }}{\cos ec{58}^{\circ }}}$

Answer 1

${\displaystyle \frac{3{\sin 72}^{\circ }}{{\cos 18}^{\circ }}-\frac{{\sec 32}^{\circ }}{\cos ec{58}^{\circ }}}$

= ${\displaystyle \frac{3\sin ({90}^{\circ }-{18}^{\circ })}{{\cos 18}^{\circ }}-\frac{\sec ({90}^{\circ }-{58}^{\circ })}{\cos ec{58}^{\circ }}}$

= ${\displaystyle \frac{3{\cos 18}^{\circ }}{{\cos 18}^{\circ }}-\frac{\cos ec{58}^{\circ }}{\cos ec{58}^{\circ }}}$

= 3 – 1

= 2