Question

Write the expression as the sine, cosine, or tangent of an angle. cos 8x cos 2x - sin 8x sin 2x

Answer 1

Sum and Difference Formula for Cosine: cos(α±β)= cosαcosβ ∓ sinαsinβ
cos(8x+2x)=cosαcosβ-sinαsinβ
cos(10x)=cosαcosβ-sinαsinβ

Answer 2

cos (A - B) = cos 6 x

Explanation:

given equation,

= cos 8 x . cos 2 x - sin 8 x . sin 2 x

using identity

cos (A - B) = cos (A) . cos(B) - sin (A) . sin(B)...................(1)

cos 8 x . cos 2 x - sin 8 x . sin 2 x......................................(2)

comparing both the equation (1) and (2)

we get ,

A = 8 x B = 2 x

hence, from the above identity we can see that

cos (A - B) = cos (8 x - 2 x)

cos (A - B) = cos 6 x