Write the expression as the sine, cosine, or tangent of an angle.
sin9x cosx - cos9x sinx

Solution:

Given: Expression is sin9x cosx - cos9x sinx

Here we have the difference of 2 angles 9x and x.

The difference formula is the most used one in trigonometry.

sin(a - b) = sina cosb - cosa sinb --- (1)

By comparing, we get a = 9x and b = x

Substitute the values of a and b in equation (1)

⇒ sin9x cosx - cos9x sinx = sin(9x - x)

⇒ sin9x cosx - cos9x sinx = sin8x

Write the expression as the sine, cosine, or tangent of an angle.
sin9x cosx - cos9x sinx

Summary:

The value of sin9x cosx - cos9x sinx is sin8x.