Question

Evaluate
$\frac{\sin {90}^{\circ }}{\cos {45}^{\circ }}+\frac{1}{\cos ec{30}^{\circ }}$

Answer 1

We know that $\sin {90}^{\circ }=1,\cos {45}^{\circ }=\frac{1}{\sqrt{2}},\csc {30}^{\circ }=2$

$\frac{\sin {90}^{\circ }}{\cos {45}^{\circ }}+\frac{1}{\csc {30}^{\circ }}$

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

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