Question

$\frac{\sin {36}^{\circ }}{\cos {54}^{\circ }}$ = ___

• A. $0$
• B. $1$
• C. $\frac{2}{3}$
• D. $\frac{3}{2}$

Answer 1

Answer: (B)

$1$

We know that $\sin \left(A\right)=\cos (\frac{\pi }{2}-A)$ where $\frac{\pi }{2}={90}^o$
As ${54}^o={90}^o-{36}^o$
we have $\frac{\sin \left({36}^o\right)}{\cos \left({54}^o\right)}=\frac{\cos \left({54}^o\right)}{\cos \left({54}^o\right)}=1$