Question

Решите, что сможете, пожалуйста.
1.) sinx+sin2x+sin3x+sin4x=0
2.) 3sin^x-7sinxcosx+14cos^x-2=0
3.) 10sinx-5cosx=4
4.) 2sin5xcos6x+sinx=sin7xcos4x

Answer 1

1)sinx+sin2x+sin3x+sin4x = (sinx+sin3x)+(sin2x+sin4x) =2sin2x× cosx+2sin3x× cosx =2cosx(sin2x+sin3x) =4sin(5x/2)× cos(x/2)× cosx sin(5x/2)=0 5x/2=p n x=2p n/5cos(x/2)=0 => x/2=p /2+p n э Z => x=p +2p ncosx=0 x=p /2+p n x=p /2+p n 2p n/5 ; p (1+2n) ; p (1/2+n), n э Z.