cosx - sinx = 0
(cosx - sinx)(cosx + sinx) = 0cos^2x - sin^2x = 0(cosx + sinx)(cosx - sinx) = 0
cosx + sinx = 0 или cosx - sinx = 0
cosx + sinx = 0sinx = -cosxtanx = -1x = 3π/4 + 2πn
cosx - sinx = 0sinx = cosxtanx = 1x = π/4 + πn
Ответ: x = 3π/4 + 2πn, π/4 + πn.
cosx - sinx = 0
(cosx - sinx)(cosx + sinx) = 0
cos^2x - sin^2x = 0
(cosx + sinx)(cosx - sinx) = 0
cosx + sinx = 0 или cosx - sinx = 0
cosx + sinx = 0
sinx = -cosx
tanx = -1
x = 3π/4 + 2πn
cosx - sinx = 0
sinx = cosx
tanx = 1
x = π/4 + πn
Ответ: x = 3π/4 + 2πn, π/4 + πn.