In order to answer this question, one would need either a far more detailed description than the one given in the question, or else a brief peek at the shaded region.
I would bet money that there's a beautiful, clear drawing right there where you copied the question from, but that you decided not to share the drawing.
500 x .15 = $75.00.........................
Consider angle XZY in the attached figure. It is always 1/2 the measure of arc XY, no matter where Z may be located on the major arc XZY. This is true even when ZY is very short.
Now, consider what happens when Z falls on top of tangent point Y. The angle is still half the measure of arc XY, still 62°.
Selection C is appropriate.
_____
I apologize for any confusion caused by my choice of Z as the name of the point I added. Nothing in my explanation is intended to refer to the Z already shown in the unmodified figure.
Answer:
OPTION C: Sin C - Cos C = s - r
Step-by-step explanation:
ABC is a right angled triangle. ∠A = 90°, from the figure.
Therefore, BC = hypotenuse, say h
Now, we find the length of AB and AC.
We know that: 
and 
Given, Sin B = r and Cos B = s
⇒ 
⇒ 
Hence, the length of the side AC = rh
Now, to compute the length of AB, we use Cos B.

⇒ 
Hence, the length of the side AB = sh
Now, we are asked to compute Sin C - Cos C.

⇒ 

= s
Sin C = s


⇒ Cos C = 
Therefore, Cos C = r
So, Sin C - Cos C = s - r, which is OPTION C and is the right answer.
Logarithm properties:

According to this, we can get: