Answer
$\sqrt 3$
Work Step by Step
Step 1. Given $sin\theta=\frac{1}{2}$ with $\theta$ in Quadrant I, we have $cos^2\theta=1-sin^2\theta=1-\frac{1}{4}=\frac{3}{4}$ which gives $cos\theta=\frac{\sqrt 3}{2}$
Step 2. Use the results above, we have $tan\theta=\frac{sin\theta}{cos\theta}=\frac{\sqrt 3}{3}$
Step 3. $sec\theta=\frac{1}{cos\theta}=\frac{2\sqrt 3}{3}$
Step 4. $tan\theta+sec\theta=\frac{\sqrt 3}{3}+\frac{2\sqrt 3}{3}=\sqrt 3$
