## anonymous one year ago can anyone prove cos(a+b) = cos(a)cos(b)-sin(a)sin(b)

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1. freckles

what can we use

2. freckles

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

3. anonymous

hint: $$\textit{Product to Sum Identities} \\ \quad \\ sin({\color{brown}{ \alpha}})sin({\color{blue}{ \beta}})=\cfrac{1}{2}[cos({\color{brown}{ \alpha}}-{\color{blue}{ \beta}})\quad -\quad cos({\color{brown}{ \alpha}}+{\color{blue}{ \beta}})] \\ \quad \\ cos({\color{brown}{ \alpha}})cos({\color{blue}{ \beta}})=\cfrac{1}{2}[cos({\color{brown}{ \alpha}}-{\color{blue}{ \beta}})\quad +\quad cos({\color{brown}{ \alpha}}+{\color{blue}{ \beta}})]$$