Question

Prove that: $\frac{\sin {36}^o}{\cos {54}^o}+\frac{\cos {36}^o}{\sin {54}^o}=2$.

Answer 1

$L.H.S.$

$=\frac{sin\left({36}^{\circ }\right)}{cos\left({54}^{\circ }\right)}+\frac{cos\left({36}^{\circ }\right)}{sin\left({54}^{\circ }\right)}$

$=\frac{sin\left({36}^{\circ }\right)sin\left({54}^{\circ }\right)+cos\left({36}^{\circ }\right)cos\left({54}^{\circ }\right)}{sin\left({54}^{\circ }\right)cos\left({54}^{\circ }\right)}$

$=\frac{2cos\left({18}^{\circ }\right)}{sin\left({108}^{\circ }\right)}$

$=\frac{2cos\left({18}^{\circ }\right)}{cos\left({18}^{\circ }\right)}$

$=2$