Довести тотожність: sin (a+b) - sina*cos^3b - cosa*sin^3b = sinb*cosb*cos(a-b)

sin (a+b) - sina*cos^3b - cosa*sin^3b =sina*cosb+cosa*sinb-sina*cos^3(b)-cosa-sin^3(b)=sina*cosb(1-cos^2(b))+cosa*sinb(1-sin^2(b))=sina*cosb*sin^2(b)+cosa*sinb*cos^2(b)=sinb*cosb(sina*cosb+cosa*cosb)=sinb*cosb*cos(a+b), ч.т.д.