S=sin(x+2017\pi/2)+2sin^2(x-\pi) +cos(x+2019\pi)+cos2x= cos x + 2sin^2(x - \pi) + (-cos(x)) + cos^2(x) - sin^2(x)= cos^2x + 2sin^2(x - \pi) - sin^2xTa có : sin^2(x - \pi) = sin(x - \pi).sin(x - \pi) = (-sinx).(-sinx) = sin^2x=> S= cos^2(x) + 2sin^2(x - \pi) - sin^2x = cos^2(x) + sin^2x- sin^2x= cos^2x 

S = sin(x + 2017 * pi/2) + 2sin^2 (x - pi)cos(x + 2019pi) + cos 2x
= cos x + 2sin^2 (x - pi) +(-cos x) +cos^2x - sin^2x
= cos^2 x + 2sin^2 (x - pi) - sin^2 x
Có: 
sin^2 (x - pi) =sin(x- pi).sin(x- pi)
=(-sin x)(- sin x) = sin^2 x
=> S = cos^2 (x) + 2sin^2 (x - pi) - sin^2 x = cos^2x+ sin^2 x - sin^2 x = cos^2 x
@Sad2006