Answer
$\dfrac{1+\cot A}{\csc A}=\sin A+\cos A$
Work Step by Step
$\dfrac{1+\cot A}{\csc A}$
Substitute $\cot A$ with $\dfrac{\cos A}{\sin A}$ and $\csc A$ with $\dfrac{1}{\sin A}$:
$\dfrac{1+\cot A}{\csc A}=\dfrac{1+\dfrac{\cos A}{\sin A}}{\dfrac{1}{\sin A}}=...$
Evaluate the sum present in the numerator and simplify:
$...=\dfrac{\dfrac{\sin A+\cos A}{\sin A}}{\dfrac{1}{\sin A}}=\sin A+\cos A$
