Question

Prove that cos${72}^{\circ }$ cot${18}^{\circ }$ = cos${18}^{\circ }$

Answer 1

cos${72}^{\circ }$ = cos(${90}^{\circ }-{18}^{\circ }$) = sin${18}^{\circ }$

$\therefore$ cos${72}^{\circ }$ cot${18}^{\circ }$ = sin${18}^{\circ }$ $\frac{cos{18}^{\circ }}{sin{18}^{\circ }}$ = $cos{18}^{\circ }$