# If sin theta - cos theta = 1/2 , what is the value of sin theta + cos theta?

Jun 19, 2017

$\sin t + \cos t = \pm \frac{\sqrt{7}}{2}$

#### Explanation:

${\left(\sin t - \cos t\right)}^{2} = 1 - 2 \sin t . \cos t$
${\left(\sin t + \cos t\right)}^{2} = 1 + 2 \sin t . \cos t$
${\left(\sin t - \cos t\right)}^{2} + {\left(\sin t + \cos t\right)}^{2} = 2$
${\left(\sin t - \cos t\right)}^{2} = {\left(\frac{1}{2}\right)}^{2} = \frac{1}{4}$
${\left(\sin t + \cos t\right)}^{2} = 2 - \frac{1}{4} = \frac{7}{4}$
$\left(\sin t + \cos t\right) = \pm \frac{\sqrt{7}}{2}$