Question

Verify the Identity. cos(α - β) - cos(α + β) = 2 sin α sin β

Answer 1

well.. just expand both cos(α - β) and cos(α + β) and see what you get

Answer 2

recall \(\bf cos({\color{brown}{ \alpha}} + {\color{blue}{ \beta}})= cos({\color{brown}{ \alpha}})cos({\color{blue}{ \beta}})- sin({\color{brown}{ \alpha}})sin({\color{blue}{ \beta}})
\\ \quad \\

cos({\color{brown}{ \alpha}} - {\color{blue}{ \beta}})= cos({\color{brown}{ \alpha}})cos({\color{blue}{ \beta}}) + sin({\color{brown}{ \alpha}})sin({\color{blue}{ \beta}})\)

expand, simplify, be happy, eat ice-cream