1. sin3x+sin5x=sin4x 2. 3sinx+4cosx=3 3.sin(^2)2x+sin(^2)3x+sin(^2)4x+(^2)5x=2...

Question

1. sin3x+sin5x=sin4x 2. 3sinx+4cosx=3 3.sin(^2)2x+sin(^2)3x+sin(^2)4x+(^2)5x=2 4.cos2x=cosx+sinx

Answer 1

1. SIN3X+SIN5X=SIN4X

2sin4xcosx-sin4x=0

sin4x(2cosx-1)=0

sin4x=0 или 2cosx-1=o

4x=pi*n

x=pi*n/4

cosx=1/2

x=+-pi/3+2pi*n

Answer 2

4) cos2x=cosx+sinx=cos² x - sin ² x - cosx+sinx= (cosx-sinx)(cosx+sinx)-cosx+sinx=cosx-sinx