Answer: The correct option is (c) sin 44°.
Step-by-step explanation: We are given to write the following expression as the sine, cosine or tangent of an angle :
[tex]T=\sin 57^\circ\cos13^\circ-\cos57^\circ\sin13^\circ.[/tex]
We will be using the following trigonometric formula :
[tex]\sin (A+B)=\sin A\cos B-\cos A\sin B.[/tex]
Therefore, we get
[tex]T\\\\=\sin 57^\circ\cos13^\circ-\cos57^\circ\sin13^\circ\\\\=\sin(57^\circ-13^\circ)\\\\=\sin 44^\circ.[/tex]
Thus, the required expression can be written in sine of an angle of measure 44°.
Option (c) is CORRECT.
