[tex]sin(a+b)*sin(a-b)=
[/tex]
[tex](sina*cosb+sinb*cosa)*(sina*cosb-sinb*cosa)[/tex]=
[tex]=sin^{2} a*cos^{2} b-sina*sinb*cosa*cosb+sina*sinb*cosa*cosb[/tex]
[tex]-sin^{2} b*cos^{2} a[/tex]=
[tex]=sin^{2} a*(1-sin^{2}b )-sin^{2} b*(1-sin^{2} a)=
[/tex]
[tex]=sin^{2}a-sin^{2} a*sin^{2} b-sin^{2} b+sin^{2} a*sin^{2} b[/tex]
[tex]=sin^{2} a-sin^{2} b[/tex]
[tex]sin^{2} x+cos^{2} x=1 rezulta cos^{2} x=1-sin^{2} x
[/tex]