Question

Write the given expression as a single trigonometric function.

sin(42°)cos(17°) – cos(42°)sin(17°)
a.cos⁡(59°)
b.sin⁡(59°)
c.cos⁡(25°)
d. sin⁡(25°)

Answer 1

The given trigonometric expression simplifies to sin(25°) using the sine difference identity, making the correct answer d. sin(25°).

Step-by-step explanation:

The expression given, sin(42°)cos(17°) − cos(42°)sin(17°), can be rewritten using the trigonometric identity for the sine of the difference between two angles.

According to identity number 10 from our reference information, sin (a ± β) = sin a cos β ± cos a sin β. This means the expression is equal to sin(42° − 17°), which simplifies to sin(25°). Therefore, the correct answer is d. sin(25°).