If $\tan A = \dfrac{1}{\sqrt3}$, find the value of $\dfrac{\sin A + \cos A}{\text{cosec}\,A}$.
Step-by-Step Solution
Key Concept: Identify the standard angle, find all needed ratios, then substitute.
$\tan A=\dfrac{1}{\sqrt3}\Rightarrow A=30^\circ$. [1.0 Mark]
$\sin30^\circ=\dfrac12,\ \cos30^\circ=\dfrac{\sqrt3}{2},\ \text{cosec}\,30^\circ=2$. [1.0 Mark]
$\dfrac{\sin A+\cos A}{\text{cosec}\,A}=\dfrac{\frac12+\frac{\sqrt3}{2}}{2}=\dfrac{1+\sqrt3}{4}$. [1.0 Mark]
Correct Answer: