Question

sinx-sin3x=cos2xsin3x Ответ : x=$frac{ pi }{4} + frac{ pi }{2} ; x= pi n$

Answer 1

$sinx-sin3x=cos2xsin3x \ -2cos2xsinx=cos2xsin3x \ cos2x(sin3x+2sinx)=0 \ \ 1) \ cos2x=0 \ 2x= dfrac{ pi }{2}+ pi k \ x= dfrac{ pi }{4}+ dfrac{ pi k}{2}; k in Z \ \ 2) \ sin3x+2sinx=0 \ 3sinx-4sin^3x+2sinx=0 \ 5sinx-4sin^3x=0 \ sinx(5-4sin^2x)=0 \ \ sinx=0 \ x= pi k; k in Z \ \ 5-4sin^2x=0 \ sin^2x= dfrac{5}{4} \ sinx= dfrac{ sqrt{5} }{2} notin [-1; 1]$

Ответ: $left [begin{array}{I} x= dfrac{ pi }{4}+ dfrac{ pi k}{2}; k in Z \x= pi k; k in Z end{array}}$