Question

Write the expression as the sine, cosine, or tangent of an angle. sin 8x cos x - cos 8x sin x

Answer 1

sin(8x)cos(x) - cos(8x)sin(x)

identity being used: -cos(s)sin(t) + cos(t)sin(s) = sin(s-t)
sin(8x)cos(x) - cos(8x)sin(x) --> simplified = sin(8x-x)
sin(8x-x) is simplified to --> sin (7x)
sin(8x)cos(x) - cos(8x)sin(x) = sin(7x)

Answer 2

sin(7x)

Explanation:

sin 8x cos x - cos 8x sin x

We use identity

sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

We have 8x in the place of 'a' and x in the place of 'b'

sin(8x-x) = sin 8x cos x - cos 8x sin x

So sin(a-b) becomes sin(8x-x)

sin(8x-x) = sin(7x)

So sin 8x cos x - cos 8x sin x= sin(7x)