Question

Упростите выражение:
1) sinX*cosX*tgX
2) sin^2t - cos^2t/ctg(-t)tgt
3) cos2X-sin^2x/2sin^2x-cos^2x

Answer 1

1) sinx*cosx*(sinx/cosx) = sin^2(x)
2) (sin^2(t) - cos^2(t))/(cost*sint/sint*cost) = sin^2(t) - cos^2(t) = -(cos^2(t) - sin^2(t)) = -cos(2t)
3) (cos(2x) - sin^2(x)) / (2sin^2(x) - cos^2(x)) = (cos^2(x) - sin^2(x) - sin^2(x)) / (2sin^2(x) - cos^2(x)) = (cos^2(x) - 2sin^2(x))/(2sin^2(x) - cos^2(x)) = -1