Question

2sinx-3cosx=0 и cosx+sinx=cos2xзаранее спасибо

Answer 1

2sinx-3cosx=0
tg(x)=3/2
x=artg(3/2)

x=56.03 градуса

cos(x)+sin(x)=2cos(2x)
cos(x)+sin(x)=cos^2(x)-sin^2(x)
cos(x)+sin(x)=(cos(x)-sin(x))(cos(x)+sin(x))
(cos(x)-sin(x)-1)(cos(x)+sin(x)=0

cos(x)+sin(x)=0

tg(x)=-1
x=-п/4+2пк

cos(x)-sin(x)-1=0
cos^2(x)=1+2sin(x)+sin^2(x)
1-sin^2(x)=1+2sin(x)+sin^2(x)
2sin(x)+2sin^2(x)=0
2sin(x)(1+sin(x))=0

sin(x)=0
x=0+2пк

1+sin(x)=0
sin(x)=-1
x=-п/2+2пк