Answer
$\dfrac{\sin t+\tan t}{\tan t}=\cos t+1$
Work Step by Step
$\dfrac{\sin t+\tan t}{\tan t}$
Substitute $\tan t$ with $\dfrac{\sin t}{\cos t}$:
$\dfrac{\sin t+\tan t}{\tan t}=\dfrac{\sin t+\dfrac{\sin t}{\cos t}}{\dfrac{\sin t}{\cos t}}=...$
Evaluate the sum present in the numerator and simplify:
$...=\dfrac{\dfrac{(\sin t)(\cos t)+\sin t}{\cos t}}{\dfrac{\sin t}{\cos t}}=\dfrac{\sin t\cos t+\sin t}{\sin t}=\cos t+1$
