Write the expression as the sine, cosine, or tangent of an angle.
cos8x cos2x - sin8x sin2x

Solution:

Given:

Expression is cos 8x cos 2x - sin 8x sin 2x,

which is of the form

cos A cos B - sin A sin B

= cos (A + B),

which is a compound angle formula of trigonometric ratios.

Here,

A = 8x and B = 2x.

Substituting these values in the formula we get,

cos 8x cos 2x - sin 8x sin 2x

= cos (8x + 2x)

= cos 10x

Write the expression as the sine, cosine, or tangent of an angle.
cos8x cos2x - sin8x sin2x

Summary:

The expression for the given trigonometric function, cos 8x cos 2x - sin 8x sin 2x, is cos 10x.