Pre- calc question

Question

rewrite in terms of 𝜶 only cos(𝛼 + 𝛽) cos 𝛽 + sin(𝛼 + 𝛽)(sin 𝛽)

Answer 1

I call this trigonometry. expand both cos(a+b) and sin(a+b)

then with algebra, have the expression=cos(a)*(cos²b+sin²b)-sin(a)*sin(b)*cos(b)+sin(a)*sin(b)*cos(b)

which nicely = cos(a)