Question

Simplify $\frac{\sin {35}^{\circ }}{\cos {55}^{\circ }}+\frac{\cos {55}^{\circ }}{\sin {35}^{\circ }}-2{\cos }^2{60}^{\circ }$

Answer 1

$\frac{\sin 35°}{\cos 55°}+\frac{\cos 55°}{\sin 35°}-2{\cos }^{2}60°$

$=\frac{\sin (90°-55°)}{\cos 55°}+\frac{\cos (90°-35°)}{\sin 35°}-2\times {\left(\frac{1}{2}\right)}^2$

$=\frac{\cos 55°}{\cos 55°}+\frac{\sin 35°}{\sin 35°}-2\times \frac{1}{4}$

$=1+1-\frac{1}{2}$

$=2-\frac{1}{2}$

$=\frac{3}{2}.$

Hence, the answer is $\frac{3}{2}.$