Question

Evaluate tan45/sin30 . In your final answer, include all calculations.

Answer 1

From the identity $\displaystyle{ \tan x= \frac{\sin x}{\cos x}$, and from the values:

                 $\sin45^{\circ}=\cos45^{\circ}= \frac{ \sqrt{2}}{2}$,

we have: $\displaystyle{ \tan 45^{\circ}= \frac{\sin 45^{\circ}}{\cos 45^{\circ}}= \frac{ \frac{ \sqrt{2}}{2}}{\frac{ \sqrt{2}}{2}} =1$.


We also know that $\sin30^{\circ}= \frac{1}{2}$.


Thus, $\displaystyle{ \frac{\tan 45^{\circ}}{\sin30^{\circ}} = \frac{1}{\frac{1}{2}}=2.$



Answer: 2