Question

can anyone prove
cos(a+b) = cos(a)cos(b)-sin(a)sin(b)

Answer 1

what can we use

Answer 2

like if we should do this from scratch I suggest distance formula...
but if we can use other identities this makes the problem a bit easier

Answer 3

hint: \(\textit{Product to Sum Identities}
\\ \quad \\

sin({\color{brown}{ \alpha}})sin({\color{blue}{ \beta}})=\cfrac{1}{2}[cos({\color{brown}{ \alpha}}-{\color{blue}{ \beta}})\quad -\quad cos({\color{brown}{ \alpha}}+{\color{blue}{ \beta}})]
\\ \quad \\

cos({\color{brown}{ \alpha}})cos({\color{blue}{ \beta}})=\cfrac{1}{2}[cos({\color{brown}{ \alpha}}-{\color{blue}{ \beta}})\quad +\quad cos({\color{brown}{ \alpha}}+{\color{blue}{ \beta}})]\)