Question

Simplify $\frac{\sin {36}^{\circ }}{\cos {54}^{\circ }}-\frac{\tan {54}^{\circ }}{\cot {36}^{\circ }}$

Answer 1

$\frac{\sin 36°}{\cos 54°}-\frac{\tan 54°}{\cot 36°}=\frac{\sin (90°-54°)}{\cos 54°}-\frac{\tan (90°-36°)}{\cot 36°}$

$=\frac{\cos 54°}{\cos 54°}-\frac{\cot 36°}{\cot 36°}$

$=1-1$

$=0.$

Hence, the answer is $0.$