Question

упростите выражение sin ^3 a cos a-sin a cos ^3 a​

Answer 1

sin ^3 α cos α-sin α cos ^3 α​=

= sin α cos α*(sin² α -cos² α​) =

= sin α cos α  (-cos 2α) = (2*sin α cos α  (-cos 2α) ) /2 =

= (- sin2αcos2α) /2 = 2(- sin2αcos2α) /4 = (- sin 4α)/4

Answer 2

$Sin^{3}\alpha Cos\alpha -Sin\alpha Cos^{3}\alpha=Sin\alpha Cos\alpha(Sin^{2}\alpha -Cos^{2}\alpha )=Sin\alpha Cos\alpha*(-Cos2\alpha)=-\frac{2Sin\alpha Cos\alpha Cos2\alpha}{2} =-\frac{Sin2\alpha Cos2\alpha}{2}=-\frac{2Sin2\alpha Cos2\alpha}{4}=-\frac{Sin4\alpha}{4}=-0,25Sin4\alpha$