# Express 10sin(ƒÖ.t+ƒÎ�€4) in the form AsinƒÖ.t + BcosƒÖ.t

Your symbols are illegible, with things like Euros and capital O-umlauts. Can you possible retype with different symbols?

## Certainly! I apologize for the confusion. Let's retype the expression using commonly-used symbols:

Express 10sin(ωt+φ/4) in the form Asin(ωt) + Bcos(ωt).

To express the given expression in the desired form, we need to make use of the trigonometric identity sin(α + β) = sinαcosβ + cosαsinβ.

Given: 10sin(ωt + φ/4)

Using the trigonometric identity sin(α + β) = sinαcosβ + cosαsinβ, we can rewrite the expression as:

10sin(ωt)cos(φ/4) + 10cos(ωt)sin(φ/4)

Now, let's simplify further using the following trigonometric identities:

sin(φ/4) = √2/2

cos(φ/4) = √2/2

Now, we can rewrite the expression as:

(10/2)sin(ωt) + (10/2)cos(ωt)

Finally, we can express it in the desired form:

Asin(ωt) + Bcos(ωt)

Where:

A = 10/2 = 5

B = 10/2 = 5

So, 10sin(ωt + φ/4) can be expressed as 5sin(ωt) + 5cos(ωt).