Question

Use identities to write the expression as a single function of x or θ:

Answer 1

`\frac{\sqrt[]{2}}{2}(\sin x\text{ + cos x)}`

Step-by-step 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:

`\sin (A\text{ + B) = sinAcosB + cosAsin B}`

We apply the same here as follows:

`\sin (x+45)\text{ = sinxcos45 + cosxsin45}`

Recall:

`\sin \text{ 45 = cos 45 = }\frac{\sqrt[]{2}}{2}`

We substitute this into the expression above

We have that as:

`\frac{\sqrt[]{2}}{2}(\sin x\text{ + cos x)}`