Question
prove sin(α+β)sin(α-β)=cos^2β-cos^2α
Answers
Steve
sin(a+b)sin(a-b)
(aina cosb + cosa sinb)(sinacosb - cosa sinb)
sin^2acos^2b + sinacosasinbcosb - sinacosasinbcosb - cos^2asin^2b)
(1-cos^2a)cos^2b - (1-cos^2b)cos^2a
cos^2b - cos^acos^b - cos^2a + cos^2acos^2b
cos^2b - cos^2a
(aina cosb + cosa sinb)(sinacosb - cosa sinb)
sin^2acos^2b + sinacosasinbcosb - sinacosasinbcosb - cos^2asin^2b)
(1-cos^2a)cos^2b - (1-cos^2b)cos^2a
cos^2b - cos^acos^b - cos^2a + cos^2acos^2b
cos^2b - cos^2a