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 expression as a single trigonometric function sin(42°)cos(17°) – cos(42°)sin(17°) is d. sin(25°) . Therefore , d. sin(25°) is correct.

To simplify the given expression sin(42°)cos(17°) - cos(42°)sin(17°) into a single trigonometric function.

we can use the trigonometric angle sum identity for sine

sin(A−B)=sinAcosB − cosAsinB

Comparing this identity with the given expression, we can identify

A=42° and B=17°.

Therefore, the given expression can be expressed as:

sin(42°−17°)

Now, we simplify the angle:

sin(25°)

So, the given expression is equivalent to sin(25°). Therefore, the correct answer is: d. sin(25°)