Question

Aratati ca sin² a - sin²b=sin(a+b) sin (a-b)

Answer 1

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


[tex]sin^{2} x+cos^{2} x=1  rezulta cos^{2} x=1-sin^{2} x [/tex]