Sin (2x+П: 3) = 1

tg (x-П: 4) >-1

Sin (pi/4) = cos (pi/4) = sqrt (2) / 2

tg (x-pi/4) = sin (x-pi/4) / cos (x-pi/4) = (sin (x) cos (pi/4) - cos (x) sin (pi/4)) / (cos (x) cos (pi/4) + sin (x) sin (pi/4)) =

= (sin (x) - cos (x)) / (sin (x) + cos (x))

tg (x+pi/4) = (sin (x) cos (pi/4) + cos (x) sin (pi/4)) / (cos (x) cos (pi/4) - sin (x) sin (pi/4)) =

= (sin (x) + cos (x)) / (cos (x) - sin (x))

tg (x-pi/4) - tg (x+pi/4) = (sin (x) - cos (x)) / (sin (x) + cos (x)) + (sin (x) + cos (x)) / (sin (x) - cos (x)) =

= ((sin (x) - cos (x)) ^2 + (sin (x) + cos (x)) ^2) / (sin^2 (x) - cos^2 (x)) =

= - (2*sin^2 (x) + 2*cos^2 (x)) / (cos^2 (x) - sin^2 (x)) = - 2/cos (2x)