Упростить: (3sinx-5cosx)^2+(5sinx+3cosx)^2=

Question

Упростить:
(3sinx-5cosx)^2+(5sinx+3cosx)^2=

Answer 1

(3sinx-5cosx)^2+(5sinx+3cosx)^2= 9sin^2(x)-
-30sinxcosx+25cos^2(x)+25sin^2(x)+30cosxsinx+9cos^2(x)=
=9(sin^2(x)+cos^2(x))+25(cos^2(x)+sin^2(x))=9*1+25*1=34