How can I simplify sinx-cosx+sin (x+pi/2)-cos (x+3pi/2)?

Answer 1

sin x - cos x + sin x*cos(pi/2) + cos x* sin(pi/2) - [ cos x * cos(3*pi/2) - sinx * sin(3*pi/2) ]

sin x - cos x + 0 + cos x - [ 0 + sin x] =

sin x - cos x + cos x - sin x

= 0

zer0