Hello Shakyiagrooms. We know:
[tex]\sin(\frac{\pi}{4}) = \frac{1}{\sqrt{2}}[/tex]
AND
[tex]\cos(\frac{\pi}{4}) = \frac{1}{\sqrt{2}}[/tex]
By knowing this, we can set the problem up as the following:
[tex]\frac{1}{\sqrt{2}} + \frac{1}{\sqrt{2}}[/tex]
Now we can add them since they have the same denominators:
[tex]\frac{1}{\sqrt{2}} +\frac{1}{\sqrt{2}} = \frac{2}{\sqrt{2}}[/tex]
Now we have to rationalize the radical denominator [tex]\frac{2}{\sqrt{2}}[/tex]. We do this by multiplying [tex]\frac{2}{\sqrt{2}}[/tex] by [tex]\frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\frac{2}{\sqrt{2}}[/tex]
[tex]\frac{2}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{2\sqrt{2}}{\sqrt{4}}[/tex]
[tex]\frac{2\sqrt{2}}{\sqrt{4}} = \frac{2\sqrt{2}}{2} = \sqrt{2} [/tex]
So our answer "Drum Roll Please" =
[tex]\sin(\frac{\pi}{4}) + \cos(\frac{\pi}{4}) = \sqrt{2}[/tex]
