Answer:
[tex]\frac{\sqrt[]{2}}{2}(\sin x\text{ + cos x)}[/tex]
Explanation:
Here, by the use of trigonometric identities, we want to write the given expression as a single function of x or theta
Mathematically, we know that:
[tex]\sin (A\text{ + B) = sinAcosB + cosAsin B}[/tex]
We apply the same here as follows:
[tex]\sin (x+45)\text{ = sinxcos45 + cosxsin45}[/tex]
Recall:
[tex]\sin \text{ 45 = cos 45 = }\frac{\sqrt[]{2}}{2}[/tex]
We substitute this into the expression above
We have that as:
[tex]\frac{\sqrt[]{2}}{2}(\sin x\text{ + cos x)}[/tex]
