Answer
$-\frac{\sqrt 5}{5}$
Work Step by Step
Step 1. Given $tan\theta=-\frac{1}{2}$ and $\theta$ in Quadrant II, use the Pythagorean Identify $tan^2\theta+1=sec^2\theta$ we have $sec^2=1+\frac{1}{4}=\frac{5}{4}$ which gives $cos^2\theta=\frac{4}{5}$ and $cos\theta=-\frac{2\sqrt 5}{5}$
Step 2. Again use the Pythagorean Identify $sin^2\theta=1-cos^2\theta=1-\frac{4}{5}=\frac{1}{5}$ we get $sin\theta=\frac{\sqrt 5}{5}$
Step 3. We find $sin\theta+cos\theta=-\frac{\sqrt 5}{5}$
