1)sin(x+a)*sin(x-a)= (sinx*cosa+cosx*sina)*(sinx*cosa-cosx*sina)=sin^2(x)*cos^2(a)-sinx*cosa*cosx*sina+cosx*sina*sinx*cosa-cos^2(x)*sin^2(a)=sin^2(x)*cos^2(a)-cos^2(x)*sin^2(a)=
(sin(x)*cos(a)-cos(x)*sin(a))*(sin(x)*cos(a)+cos(x)*sin(a))= sin(x +- a)
^^^^^^^^^^^^^^^
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a^2-b^2= (a-b)*(a+b)
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1)sin(x+a)*sin(x-a)= (sinx*cosa+cosx*sina)*(sinx*cosa-cosx*sina)=sin^2(x)*cos^2(a)-sinx*cosa*cosx*sina+cosx*sina*sinx*cosa-cos^2(x)*sin^2(a)=sin^2(x)*cos^2(a)-cos^2(x)*sin^2(a)=
(sin(x)*cos(a)-cos(x)*sin(a))*(sin(x)*cos(a)+cos(x)*sin(a))= sin(x +- a)
^^^^^^^^^^^^^^^
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a^2-b^2= (a-b)*(a+b)