sin(a+b)sin(a-b) =sin^2 a - sin^2 b= cos^2 b -cos^2 acos(a+b)cos(a-b) = cos^2 a-sin^2 b= cos^2 b -sin^2 a
热心网友
sin(a+b)sin(a-b) =sin^2 a - sin^2 b= cos^2 b -cos^2 a证：sin(a+b)sin(a-b)=(1/2)(cos2b-cos2a)=(1/2)[(1-cos2a)-(1-cos2b)]=(1/2)[2(sina)^2-2(sinb)^2]=(sina)^2-(sinb)^2=[1-(sinb)^2]-[1-(sina)^2]=(cosb)^2-(cosa)^2cos(a+b)cos(a-b) = cos^2 a-sin^2 b= cos^2 b -sin^2 a证：cos(a+b)cos(a-b)=(1/2)(cos2a+cos2b)=(1/2)[-(1-cos2a)+(1+cos2b)]=(1/2)[-2(sina)^2+2(cosb)^2]=(cosb)^2-(sina)^2=[1-(sina)^2]-[1-(cosb)^2]=(cosa)^2-(sinb)^2。