Упростить выражение

1. cos^2x - (ctg^2+1) * sin^2x

2. sin^2x-1/1+sinx + tgx*ctgx

3. sinx/1+cosx / + sinx/1-cosx

4. ctg^2x * (cos^2x-1) + 1

5. cosx/1+sinx + cosx/1-sinx

6. tgx+1/1+ctgx

1. = cos^2x-cos^2x+sin^2x=sin^2x

2. = (sinx-1) * (sinx+1) / (1+sinx) + 1 = sinx-1+1=sinx

3. = (sinx * (1-cosx) + sinx * (1+cosx)) / (1+cosx) * (1-cosx) = (sinx-sinx*cosx+sinx+sinx*cosx) / (1-cos^2x) = 2*sinx/sin^2x=2/sinx

4. = ctg^2x * (-sin^2x) + 1=-cos^2x+1=sin^2x

5. = (cosx * (1-sinx) + cosx * (1+sinx)) / (1+sinx) (1-sinx) = (cosx-cosx*sinx+cosx+cosx*sinx) / (1-sin^2x) =

2cosx/cos^2x=2/cosx

6. = ((sinx+cosx) / cosx) / (cosx+sinx) / sinx=sinx/cosx=tgx